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Free Form | Lớp 9 | Tính
$ \sqrt{45.80}$ | $ \sqrt{45.80}=\sqrt{3600}=60$ | https://khoahoc.vietjack.com/question/1008443 | ### Câu hỏi:
Tính
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>45.80</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>45.80</mn></msqrt><mo>=</mo><msqrt><mn>3600</mn></msqrt><mo>=</mo><mn>60</mn></math>
|
Free Form | Lớp 9 | Tính
$ \sqrt{2,5.14,4}$ | $ \sqrt{2,5.14,4}=\sqrt{36}=6$ | https://khoahoc.vietjack.com/question/1008445 | ### Câu hỏi:
Tính
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn><mo>,</mo><mn>5.14</mn><mo>,</mo><mn>4</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn><mo>,</mo><mn>5.14</mn><mo>,</mo><mn>4</mn></msqrt><mo>=</mo><msqrt><mn>36</mn></msqrt><mo>=</mo><mn>6</mn></math>
|
Free Form | Lớp 9 | Tính
$ \sqrt{21,{8}^{2}-18,{2}^{2}}$ | $ \sqrt{21,{8}^{2}-18,{2}^{2}}=\sqrt{\left(21,8-18,2\right)\left(21,8+18,2\right)}=\sqrt{3,6.40}=\sqrt{144}=12$ | https://khoahoc.vietjack.com/question/1008448 | ### Câu hỏi:
Tính
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>21</mn><mo>,</mo><msup><mn>8</mn><mn>2</mn></msup><mo>−</mo><mn>18</mn><mo>,</mo><msup><mn>2</mn><mn>2</mn></msup></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>21</mn><mo>,</mo><msup><mn>8</mn><mn>2</mn></msup><mo>−</mo><mn>18</mn><mo>,</mo><msup><mn>2</mn><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mfenced><mrow><mn>21</mn><mo>,</mo><mn>8</mn><mo>−</mo><mn>18</mn><mo>,</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mn>21</mn><mo>,</mo><mn>8</mn><mo>+</mo><mn>18</mn><mo>,</mo><mn>2</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mn>3</mn><mo>,</mo><mn>6.40</mn></msqrt><mo>=</mo><msqrt><mn>144</mn></msqrt><mo>=</mo><mn>12</mn></math>
|
Free Form | Lớp 9 | <p>Tính</p>
<p>$ \sqrt{117,{5}^{2}-26,{5}^{2}-1440}$</p> | $ \begin{array}{l}\sqrt{117,{5}^{2}-26,{5}^{2}-1440}=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-1440}\\ =\sqrt{91.144-10.144}=\sqrt{81.144}=\sqrt{81}.\sqrt{144}=9.12=108\end{array}$
<div> </div> | https://khoahoc.vietjack.com/question/1008451 | ### Câu hỏi:
<p>Tính</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>117</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>26</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>1440</mn></msqrt></math></p>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>117</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>26</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>1440</mn></msqrt><mo>=</mo><msqrt><mfenced><mrow><mn>117</mn><mo>,</mo><mn>5</mn><mo>−</mo><mn>26</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mfenced><mrow><mn>117</mn><mo>,</mo><mn>5</mn><mo>+</mo><mn>26</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>−</mo><mn>1440</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>91.144</mn><mo>−</mo><mn>10.144</mn></msqrt><mo>=</mo><msqrt><mn>81.144</mn></msqrt><mo>=</mo><msqrt><mn>81</mn></msqrt><mo>.</mo><msqrt><mn>144</mn></msqrt><mo>=</mo><mn>9.12</mn><mo>=</mo><mn>108</mn></mtd></mtr></mtable></math>
<div> </div>
|
Free Form | Lớp 9 | Tính
$ \sqrt{146,{5}^{2}-109,{5}^{2}+27.256}$ | $ \begin{array}{l}\sqrt{146,{5}^{2}-109,{5}^{2}+27.256}\\ =\sqrt{\left(146,5-109,5\right).\left(146,5+109,5\right)+27.256}\\ =\sqrt{37.256+27.256}=\sqrt{\left(37+27\right).256}\\ =\sqrt{64.256}=\sqrt{64}.\sqrt{256}=8.16=128\end{array}$ | https://khoahoc.vietjack.com/question/1008453 | ### Câu hỏi:
Tính
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>146</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>109</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mn>27.256</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>146</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>109</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mn>27.256</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mfenced><mrow><mn>146</mn><mo>,</mo><mn>5</mn><mo>−</mo><mn>109</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>.</mo><mfenced><mrow><mn>146</mn><mo>,</mo><mn>5</mn><mo>+</mo><mn>109</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>+</mo><mn>27.256</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>37.256</mn><mo>+</mo><mn>27.256</mn></msqrt><mo>=</mo><msqrt><mfenced><mrow><mn>37</mn><mo>+</mo><mn>27</mn></mrow></mfenced><mn>.256</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>64.256</mn></msqrt><mo>=</mo><msqrt><mn>64</mn></msqrt><mo>.</mo><msqrt><mn>256</mn></msqrt><mo>=</mo><mn>8.16</mn><mo>=</mo><mn>128</mn></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | <p>Tính</p>
<p>$ \frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}$</p> | <p>$ \frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}=\frac{\sqrt{3}.\sqrt{2}+\sqrt{7}.\sqrt{2}}{2\sqrt{3}+2\sqrt{7}}=\frac{\sqrt{2}.\left(\sqrt{3}+\sqrt{7}\right)}{2\left(\sqrt{3}+\sqrt{7}\right)}=\frac{\sqrt{2}}{2}$</p> | https://khoahoc.vietjack.com/question/1008458 | ### Câu hỏi:
<p>Tính</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>28</mn></msqrt></mrow></mfrac><mo> </mo><mo> </mo><mo> </mo></math></p>
### Lời giải:
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>28</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>.</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt><mo>.</mo><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>7</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></p>
|
Free Form | Lớp 9 | $\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$ | $\begin{aligned}
&\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\
&=\frac{\sqrt{2}+\sqrt{3}+2+2+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\
&=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\
&=\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1+\sqrt{2}
\end{aligned}$ | https://khoahoc.vietjack.com/question/1008461 | ### Câu hỏi:
$\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$
### Lời giải:
$\begin{aligned}
&\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\
&=\frac{\sqrt{2}+\sqrt{3}+2+2+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\
&=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\
&=\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1+\sqrt{2}
\end{aligned}$
|
Free Form | Lớp 9 | <p>Tính</p>
<p>$ \sqrt{3-\sqrt{29-12\sqrt{5}}}$</p> | <p>$ \begin{array}{l}\sqrt{3-\sqrt{29-12\sqrt{5}}}=\sqrt{3-\sqrt{{3}^{2}-\mathrm{2.3.2}\sqrt{5}+{\left(2\sqrt{5}\right)}^{2}}}\\ =\sqrt{3-\sqrt{{\left(2\sqrt{5}-3\right)}^{2}}}=\sqrt{3-\left(2\sqrt{5}-3\right)}=\sqrt{6-2\sqrt{5}}\\ =\sqrt{5-2\sqrt{5}.1+1}=\sqrt{{\left(\sqrt{5}-1\right)}^{2}}=\sqrt{5}-1\end{array}$</p> | https://khoahoc.vietjack.com/question/1008465 | ### Câu hỏi:
<p>Tính</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></math></p>
### Lời giải:
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mn>3</mn><mn>2</mn></msup><mo>−</mo><mn>2.3.2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>5</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mn>.1</mn><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mtd></mtr></mtable></math></p>
|
Free Form | Lớp 9 | <p>Tính</p>
$ \sqrt{17-4\sqrt{9+4\sqrt{5}}}$ | $ \begin{array}{l}\sqrt{17-4\sqrt{9+4\sqrt{5}}}=\sqrt{17-4\sqrt{5+2\sqrt{5}.2+4}}\\ =\sqrt{17-4\sqrt{{\left(\sqrt{5}+2\right)}^{2}}}=\sqrt{17-4\left(2+\sqrt{5}\right)}\\ =\sqrt{9-4\sqrt{5}}=\sqrt{5-2\sqrt{5}.2+4}=\sqrt{{\left(\sqrt{5}-2\right)}^{2}}=\sqrt{5}-2\end{array}$ | https://khoahoc.vietjack.com/question/1008467 | ### Câu hỏi:
<p>Tính</p>
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><msqrt><mn>9</mn><mo>+</mo><mn>4</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><msqrt><mn>9</mn><mo>+</mo><mn>4</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><msqrt><mn>5</mn><mo>+</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mn>.2</mn><mo>+</mo><mn>4</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>9</mn><mo>−</mo><mn>4</mn><msqrt><mn>5</mn></msqrt></msqrt><mo>=</mo><msqrt><mn>5</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mn>.2</mn><mo>+</mo><mn>4</mn></msqrt><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ \sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$ | $ \begin{array}{l}\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}\right)}^{2}-2.2\sqrt{5}.3+{3}^{2}}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}-3\right)}^{2}}}}=\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5}-3\right)}}\\ =\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}=\sqrt{\sqrt{5}-\sqrt{{\left(\sqrt{5}-1\right)}^{2}}}=\sqrt{\sqrt{5}-\sqrt{5}+1}=\sqrt{1}=1\end{array}$ | https://khoahoc.vietjack.com/question/1008471 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.2</mn><msqrt><mn>5</mn></msqrt><mn>.3</mn><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | <p>Tính</p>
<p>$ \sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$</p> | <p>$ \begin{array}{l}\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}\right)}^{2}-2.2\sqrt{5}.3+{3}^{2}}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}-3\right)}^{2}}}}=\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5}-3\right)}}\\ =\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}=\sqrt{\sqrt{5}-\sqrt{{\left(\sqrt{5}-1\right)}^{2}}}=\sqrt{\sqrt{5}-\sqrt{5}+1}=\sqrt{1}=1\end{array}$</p> | https://khoahoc.vietjack.com/question/1008472 | ### Câu hỏi:
<p>Tính</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt></math></p>
### Lời giải:
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.2</mn><msqrt><mn>5</mn></msqrt><mn>.3</mn><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math></p>
|
Free Form | Lớp 9 | $ \left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}$ | $ \begin{array}{l}\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\\ =\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{2}.\sqrt{4-\sqrt{15}}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{8-2\sqrt{15}}\\ =\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{{\left(\sqrt{5}-\sqrt{3}\right)}^{2}}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)\\ =\left(4+\sqrt{15}\right){\left(\sqrt{5}-\sqrt{3}\right)}^{2}=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\\ =32+8\sqrt{15}-8\sqrt{15}-30=2\end{array}$ | https://khoahoc.vietjack.com/question/1008476 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>10</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow></mfenced><msqrt><mn>4</mn><mo>−</mo><msqrt><mn>15</mn></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>10</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow></mfenced><msqrt><mn>4</mn><mo>−</mo><msqrt><mn>15</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>4</mn><mo>−</mo><msqrt><mn>15</mn></msqrt></msqrt><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><msqrt><mn>8</mn><mo>−</mo><mn>2</mn><msqrt><mn>15</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>8</mn><mo>−</mo><mn>2</mn><msqrt><mn>15</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mn>32</mn><mo>+</mo><mn>8</mn><msqrt><mn>15</mn></msqrt><mo>−</mo><mn>8</mn><msqrt><mn>15</mn></msqrt><mo>−</mo><mn>30</mn><mo>=</mo><mn>2</mn></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | <p>Tính</p>
<div><span>$ \begin{array}{l}\text{\hspace{0.17em}}\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3-\sqrt{5}}\end{array}$</span></div> | <div>$ \begin{array}{l}\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3-\sqrt{5}}\\ =\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\sqrt{2}.\sqrt{3-\sqrt{5}}=\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\sqrt{6-2\sqrt{5}}\\ =\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\left(\sqrt{5}-1\right)=\left(3+\sqrt{5}\right){\left(\sqrt{5}-1\right)}^{2}\\ =\left(3+\sqrt{5}\right)\left(6-2\sqrt{5}\right)=18+6\sqrt{5}-6\sqrt{5}-10=8\end{array}$</div> | https://khoahoc.vietjack.com/question/1008482 | ### Câu hỏi:
<p>Tính</p>
<div><span><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>10</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfenced><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr></mtable></math></span></div>
### Lời giải:
<div><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>10</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfenced><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mo>=</mo><mn>18</mn><mo>+</mo><mn>6</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>6</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>10</mn><mo>=</mo><mn>8</mn></mtd></mtr></mtable></math></div>
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Free Form | Lớp 7 | Cho hình vẽ sau:
[https://video.vietjack.com/upload2/quiz_source1/2022/08/2-1660054613.png](https://video.vietjack.com/upload2/quiz_source1/2022/08/2-1660054613.png)
Điền vào chỗ trống (…) trong các câu sau:
\(\widehat {BAC}\) và \(\widehat {ACD}\) là một cặp góc …; | Hướng dẫn giải:
\(\widehat {BAC}\) và \(\widehat {ACD}\) là một cặp góc **so le trong**; | https://khoahoc.vietjack.com/question/1008483 | ### Câu hỏi:
Cho hình vẽ sau:
[https://video.vietjack.com/upload2/quiz_source1/2022/08/2-1660054613.png](https://video.vietjack.com/upload2/quiz_source1/2022/08/2-1660054613.png)
Điền vào chỗ trống (…) trong các câu sau:
\(\widehat {BAC}\) và \(\widehat {ACD}\) là một cặp góc …;
### Lời giải:
Hướng dẫn giải:
\(\widehat {BAC}\) và \(\widehat {ACD}\) là một cặp góc **so le trong**;
|
Free Form | Lớp 7 | Điền vào chỗ trống (…) trong các câu sau:
\(\widehat {BAO}\) và \(\widehat {BOC}\) là một cặp góc …; | \(\widehat {BAO}\) và \(\widehat {BOC}\) là một cặp góc **<em>đồng vị</em>**; | https://khoahoc.vietjack.com/question/1008486 | ### Câu hỏi:
Điền vào chỗ trống (…) trong các câu sau:
\(\widehat {BAO}\) và \(\widehat {BOC}\) là một cặp góc …;
### Lời giải:
\(\widehat {BAO}\) và \(\widehat {BOC}\) là một cặp góc **<em>đồng vị</em>**;
|
Free Form | Lớp 7 | Điền vào chỗ trống (…) trong các câu sau:
\(\widehat {DAC}\) và \(\widehat {ACB}\) là một cặp góc …; | Hướng dẫn giải:
\(\widehat {DAC}\) và \(\widehat {ACB}\) là một cặp góc **so le trong**; | https://khoahoc.vietjack.com/question/1008487 | ### Câu hỏi:
Điền vào chỗ trống (…) trong các câu sau:
\(\widehat {DAC}\) và \(\widehat {ACB}\) là một cặp góc …;
### Lời giải:
Hướng dẫn giải:
\(\widehat {DAC}\) và \(\widehat {ACB}\) là một cặp góc **so le trong**;
|
Free Form | Lớp 7 | Điền vào chỗ trống (…) trong các câu sau:
\(\widehat {AOD}\) và \(\widehat {OCD}\) là một cặp góc …. | Hướng dẫn giải:
\(\widehat {AOD}\) và \(\widehat {OCD}\) là một cặp góc **đồng vị**. | https://khoahoc.vietjack.com/question/1008489 | ### Câu hỏi:
Điền vào chỗ trống (…) trong các câu sau:
\(\widehat {AOD}\) và \(\widehat {OCD}\) là một cặp góc ….
### Lời giải:
Hướng dẫn giải:
\(\widehat {AOD}\) và \(\widehat {OCD}\) là một cặp góc **đồng vị**.
|
Free Form | Lớp 7 | Thực hiện phép tính: $ \frac{-3}{16}+\frac{5}{6}$ | $ \frac{-3}{16}+\frac{5}{6}=\frac{-9}{48}+\frac{40}{48}=\frac{31}{48}$ | https://khoahoc.vietjack.com/question/1008507 | ### Câu hỏi:
Thực hiện phép tính: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>−</mo><mn>3</mn></mrow><mn>16</mn></mfrac><mo>+</mo><mfrac><mn>5</mn><mn>6</mn></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>−</mo><mn>3</mn></mrow><mn>16</mn></mfrac><mo>+</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>9</mn></mrow><mn>48</mn></mfrac><mo>+</mo><mfrac><mn>40</mn><mn>48</mn></mfrac><mo>=</mo><mfrac><mn>31</mn><mn>48</mn></mfrac></math>
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Free Form | Lớp 7 | $ \frac{7}{20}-\frac{8}{15}$ | $ \frac{7}{20}-\frac{8}{15}=\frac{21}{60}-\frac{32}{60}=\frac{-11}{60}$ | https://khoahoc.vietjack.com/question/1008512 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>20</mn></mfrac><mo>−</mo><mfrac><mn>8</mn><mn>15</mn></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>20</mn></mfrac><mo>−</mo><mfrac><mn>8</mn><mn>15</mn></mfrac><mo>=</mo><mfrac><mn>21</mn><mn>60</mn></mfrac><mo>−</mo><mfrac><mn>32</mn><mn>60</mn></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>11</mn></mrow><mn>60</mn></mfrac></math>
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Free Form | Lớp 7 | Thực hiện phép tính $0,7 + \frac{4}{15}$ | $0,7 + \frac{4}{15} = \frac{7}{10} + \frac{4}{15} = \frac{21}{30} + \frac{8}{30} = \frac{29}{30}$ | https://khoahoc.vietjack.com/question/1008514 | ### Câu hỏi:
Thực hiện phép tính $0,7 + \frac{4}{15}$
### Lời giải:
$0,7 + \frac{4}{15} = \frac{7}{10} + \frac{4}{15} = \frac{21}{30} + \frac{8}{30} = \frac{29}{30}$
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Free Form | Lớp 7 | $\frac{4}{7}.\frac{5}{8}\,\,-\,\,\frac{4}{7}.\frac{1}{3}$ | $\frac{4}{7}.\frac{5}{8}-\frac{4}{7}.\frac{1}{3}=\frac{4}{7}.\left(\frac{5}{8}-\frac{1}{3}\right)=\frac{4}{7}.\frac{7}{24}=\frac{1}{6}$ | https://khoahoc.vietjack.com/question/1008517 | ### Câu hỏi:
$\frac{4}{7}.\frac{5}{8}\,\,-\,\,\frac{4}{7}.\frac{1}{3}$
### Lời giải:
$\frac{4}{7}.\frac{5}{8}-\frac{4}{7}.\frac{1}{3}=\frac{4}{7}.\left(\frac{5}{8}-\frac{1}{3}\right)=\frac{4}{7}.\frac{7}{24}=\frac{1}{6}$
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Free Form | Lớp 7 | Thực hiện phép tính $ \frac{11}{19}+\frac{19}{18}+\frac{8}{19}-\frac{1}{18}+5,2$ | $ \frac{11}{19}+\frac{19}{18}+\frac{8}{19}-\frac{1}{18}+5,2=7,2$ | https://khoahoc.vietjack.com/question/1008520 | ### Câu hỏi:
Thực hiện phép tính <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>11</mn><mn>19</mn></mfrac><mo>+</mo><mfrac><mn>19</mn><mn>18</mn></mfrac><mo>+</mo><mfrac><mn>8</mn><mn>19</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>18</mn></mfrac><mo>+</mo><mn>5</mn><mo>,</mo><mn>2</mn></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>11</mn><mn>19</mn></mfrac><mo>+</mo><mfrac><mn>19</mn><mn>18</mn></mfrac><mo>+</mo><mfrac><mn>8</mn><mn>19</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>18</mn></mfrac><mo>+</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>=</mo><mn>7</mn><mo>,</mo><mn>2</mn></math>
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Free Form | Lớp 7 | $\frac{3}{7} \cdot \frac{16}{15} - \frac{3}{7} \cdot \frac{2}{15}$ | $\frac{3}{7} \cdot \frac{16}{15} - \frac{3}{7} \cdot \frac{2}{15} = \frac{3}{7} \cdot \left( \frac{16}{15} - \frac{2}{15} \right) = \frac{2}{5}$ | https://khoahoc.vietjack.com/question/1008522 | ### Câu hỏi:
$\frac{3}{7} \cdot \frac{16}{15} - \frac{3}{7} \cdot \frac{2}{15}$
### Lời giải:
$\frac{3}{7} \cdot \frac{16}{15} - \frac{3}{7} \cdot \frac{2}{15} = \frac{3}{7} \cdot \left( \frac{16}{15} - \frac{2}{15} \right) = \frac{2}{5}$
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Free Form | Lớp 7 | Thực hiện phép tính $ \left(\frac{5}{12}:3\frac{2}{6}\right)+{\left(\frac{2}{3}-\frac{1}{2}\right)}^{2}$ | $ \left(\frac{5}{12}:3\frac{2}{6}\right)+{\left(\frac{2}{3}-\frac{1}{2}\right)}^{2}=\left(\frac{5}{12}:3\frac{2}{6}\right)+{\left(\frac{1}{6}\right)}^{2}=\frac{1}{8}+\frac{1}{36}=\frac{11}{72}$ | https://khoahoc.vietjack.com/question/1008525 | ### Câu hỏi:
Thực hiện phép tính <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>5</mn><mn>12</mn></mfrac><mo>:</mo><mn>3</mn><mfrac><mn>2</mn><mn>6</mn></mfrac></mrow></mfenced><mo>+</mo><msup><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mn>2</mn></msup></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>5</mn><mn>12</mn></mfrac><mo>:</mo><mn>3</mn><mfrac><mn>2</mn><mn>6</mn></mfrac></mrow></mfenced><mo>+</mo><msup><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mfenced><mrow><mfrac><mn>5</mn><mn>12</mn></mfrac><mo>:</mo><mn>3</mn><mfrac><mn>2</mn><mn>6</mn></mfrac></mrow></mfenced><mo>+</mo><msup><mfenced><mfrac><mn>1</mn><mn>6</mn></mfrac></mfenced><mn>2</mn></msup><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>36</mn></mfrac><mo>=</mo><mfrac><mn>11</mn><mn>72</mn></mfrac></math>
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Free Form | Lớp 7 | Thực hiện phép tính $\frac{4^2.2^3}{2^6}$ | $\frac{4^2.2^3}{2^6}=\frac{2^4.2^3}{2^6}=\frac{2^7}{2^6}=2$ | https://khoahoc.vietjack.com/question/1008529 | ### Câu hỏi:
Thực hiện phép tính $\frac{4^2.2^3}{2^6}$
### Lời giải:
$\frac{4^2.2^3}{2^6}=\frac{2^4.2^3}{2^6}=\frac{2^7}{2^6}=2$
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Free Form | Lớp 7 | Tìm $ x$: $ \frac{1}{2}+\frac{2}{3}\cdot x=\frac{4}{5}$ | $ x=\left(\frac{4}{5}-\frac{1}{2}\right):\frac{2}{3}\Rightarrow x=\frac{3}{10}.\frac{3}{2}\Rightarrow x=\frac{9}{20}$
Vậy $ x=\frac{9}{20}$ | https://khoahoc.vietjack.com/question/1008535 | ### Câu hỏi:
Tìm <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>⋅</mo><mi>x</mi><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfenced><mrow><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mo>:</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mn>3</mn><mn>10</mn></mfrac><mo>.</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>20</mn></mfrac></math>
Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>20</mn></mfrac></math>
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Free Form | Lớp 7 | Tìm x: $\frac{x}{27}=\frac{-2}{3,6}$ | $\frac{x}{27}=\frac{-2}{3,6}\Rightarrow x=\frac{-2.27}{3,6}\Rightarrow x=-15$
Vậy $x=-15$ | https://khoahoc.vietjack.com/question/1008537 | ### Câu hỏi:
Tìm x: $\frac{x}{27}=\frac{-2}{3,6}$
### Lời giải:
$\frac{x}{27}=\frac{-2}{3,6}\Rightarrow x=\frac{-2.27}{3,6}\Rightarrow x=-15$
Vậy $x=-15$
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Free Form | Lớp 7 | Tìm x: $\left| x-12 \right|-3=2014$ | $\left| x-12 \right|-3=2014\Rightarrow \left| x-12 \right|=2017\Rightarrow x\–12=2017$ hoặc $x\ –12=-2017$
$\Rightarrow x=2029$ hoặc $x=-2005$
Vậy $x=2029$ hoặc $x=-2005$ | https://khoahoc.vietjack.com/question/1008542 | ### Câu hỏi:
Tìm x: $\left| x-12 \right|-3=2014$
### Lời giải:
$\left| x-12 \right|-3=2014\Rightarrow \left| x-12 \right|=2017\Rightarrow x\–12=2017$ hoặc $x\ –12=-2017$
$\Rightarrow x=2029$ hoặc $x=-2005$
Vậy $x=2029$ hoặc $x=-2005$
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Free Form | Lớp 7 | Tìm x: $ 3\sqrt{x}+1=40$ | $ 3\sqrt{x}+1=40\Rightarrow \sqrt{x}=13\Rightarrow x=169.$
Vậy $ x=169$ | https://khoahoc.vietjack.com/question/1008547 | ### Câu hỏi:
Tìm x: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn><mo>=</mo><mn>40</mn></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn><mo>=</mo><mn>40</mn><mo>⇒</mo><msqrt><mi>x</mi></msqrt><mo>=</mo><mn>13</mn><mo>⇒</mo><mi>x</mi><mo>=</mo><mn>169.</mn></math>
Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>169</mn></math>
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Free Form | Lớp 7 | Tìm số học sinh của mỗi lớp 7A, 7B biết rằng số học sinh lớp 7A nhiều hơn số học sinh lớp 7B là 3 em. Tỉ số học sinh của hai lớp bằng $\frac{12}{11}$. | Gọi số học sinh lớp 7A là $x$, số học sinh lớp 7B là $y$ (ĐK: $x, y, z \in \mathbb{N}^*$, học sinh).
Theo đề bài ta có $\frac{x}{y} = \frac{12}{11} \Rightarrow \frac{x}{12} = \frac{y}{11} = \frac{x - y}{12 - 11} = \frac{3}{1}$
Vậy $x = 36 \Rightarrow$ Số học sinh lớp 7A là 36 học sinh
Vậy $y = 33 \Rightarrow$ Số học sinh lớp 7 B là 33 học sinh | https://khoahoc.vietjack.com/question/1008551 | ### Câu hỏi:
Tìm số học sinh của mỗi lớp 7A, 7B biết rằng số học sinh lớp 7A nhiều hơn số học sinh lớp 7B là 3 em. Tỉ số học sinh của hai lớp bằng $\frac{12}{11}$.
### Lời giải:
Gọi số học sinh lớp 7A là $x$, số học sinh lớp 7B là $y$ (ĐK: $x, y, z \in \mathbb{N}^*$, học sinh).
Theo đề bài ta có $\frac{x}{y} = \frac{12}{11} \Rightarrow \frac{x}{12} = \frac{y}{11} = \frac{x - y}{12 - 11} = \frac{3}{1}$
Vậy $x = 36 \Rightarrow$ Số học sinh lớp 7A là 36 học sinh
Vậy $y = 33 \Rightarrow$ Số học sinh lớp 7 B là 33 học sinh
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Free Form | Lớp 7 | Tìm các số $x,y,z$ biết $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}$ và $x-y+z=56.$ | Tìm các số $x,y,z$ biết $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}$ và $x-y+z=56.$
Áp dụng tính chất của dãy tỉ số bằng nhau suy ra $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}=\frac{x-y+z}{9-3+8}=\frac{56}{14}=4$
Vậy $x=36; y=12; z=32$ | https://khoahoc.vietjack.com/question/1008559 | ### Câu hỏi:
Tìm các số $x,y,z$ biết $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}$ và $x-y+z=56.$
### Lời giải:
Tìm các số $x,y,z$ biết $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}$ và $x-y+z=56.$
Áp dụng tính chất của dãy tỉ số bằng nhau suy ra $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}=\frac{x-y+z}{9-3+8}=\frac{56}{14}=4$
Vậy $x=36; y=12; z=32$
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Free Form | Lớp 7 | Số học sinh ba khối 6, 7, 8 tỉ lệ với các số 41; 29; 30. Biết rằng tổng số học sinh khối 6 và 7 là 140 học sinh. Tính số học sinh mỗi khối. | Gọi số học sinh ba khối 6, 7, 8 lần lượt là $x, y, z$ (ĐK: $x, y, z \in \mathbb{N}^*$, học sinh).
Theo đề bài ta có; $\frac{x}{41} = \frac{y}{29} = \frac{z}{30}$ và $x + y = 140$
Áp dụng tính chất của dãy tỉ số bằng nhau suy ra
$\frac{x}{41} = \frac{y}{29} = \frac{z}{30} = \frac{x + y}{41 + 29} = \frac{140}{70} = 2$
$\frac{x}{41} = 2 \Rightarrow x = 82$ (học sinh)
$\frac{y}{29} = 2 \Rightarrow y = 58$ (học sinh)
$\frac{z}{30} = 2 \Rightarrow z = 60$ (học sinh)
Vậy số học sinh khối 6, 7, 8 lần lượt là 82, 58, 60 học sinh. | https://khoahoc.vietjack.com/question/1008564 | ### Câu hỏi:
Số học sinh ba khối 6, 7, 8 tỉ lệ với các số 41; 29; 30. Biết rằng tổng số học sinh khối 6 và 7 là 140 học sinh. Tính số học sinh mỗi khối.
### Lời giải:
Gọi số học sinh ba khối 6, 7, 8 lần lượt là $x, y, z$ (ĐK: $x, y, z \in \mathbb{N}^*$, học sinh).
Theo đề bài ta có; $\frac{x}{41} = \frac{y}{29} = \frac{z}{30}$ và $x + y = 140$
Áp dụng tính chất của dãy tỉ số bằng nhau suy ra
$\frac{x}{41} = \frac{y}{29} = \frac{z}{30} = \frac{x + y}{41 + 29} = \frac{140}{70} = 2$
$\frac{x}{41} = 2 \Rightarrow x = 82$ (học sinh)
$\frac{y}{29} = 2 \Rightarrow y = 58$ (học sinh)
$\frac{z}{30} = 2 \Rightarrow z = 60$ (học sinh)
Vậy số học sinh khối 6, 7, 8 lần lượt là 82, 58, 60 học sinh.
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Free Form | Lớp 7 | Tính chu vi và diện tích của một mảnh vườn hình chữ nhật có chiều dài là 10,234 m và chiều rộng là 4,7 m (làm tròn kết quả đến hàng đơn vị) | Tính chu vi: $ \left(10,234+4,7\right).2=29,868\approx 30$ (m)
Tính diện tích: $ 10,234.4,7=48,0998\approx 48$ (m<sup>2</sup>) | https://khoahoc.vietjack.com/question/1008573 | ### Câu hỏi:
Tính chu vi và diện tích của một mảnh vườn hình chữ nhật có chiều dài là 10,234 m và chiều rộng là 4,7 m (làm tròn kết quả đến hàng đơn vị)
### Lời giải:
Tính chu vi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>10</mn><mo>,</mo><mn>234</mn><mo>+</mo><mn>4</mn><mo>,</mo><mn>7</mn></mrow></mfenced><mn>.2</mn><mo>=</mo><mn>29</mn><mo>,</mo><mn>868</mn><mo>≈</mo><mo> </mo><mn>30</mn></math> (m)
Tính diện tích: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>,</mo><mn>234.4</mn><mo>,</mo><mn>7</mn><mo>=</mo><mn>48</mn><mo>,</mo><mn>0998</mn><mo>≈</mo><mo> </mo><mn>48</mn></math> (m<sup>2</sup>)
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Free Form | Lớp 7 | $S = 1 + 2 + 2^2 + 2^3 + … + 2^{50}$ và $2^{51}$ | $S = 1 + 2 + 2^2 + 2^3 + … + 2^{50}$
ta có $2S = 2 + 2^2 + 2^3 + … + 2^{50} + 2^{51}$
$\Rightarrow 2S – S = 2^{51} - 1$
$\Rightarrow S = 2^{51} - 1$
$\Rightarrow S < 2^{51}$ | https://khoahoc.vietjack.com/question/1008582 | ### Câu hỏi:
$S = 1 + 2 + 2^2 + 2^3 + … + 2^{50}$ và $2^{51}$
### Lời giải:
$S = 1 + 2 + 2^2 + 2^3 + … + 2^{50}$
ta có $2S = 2 + 2^2 + 2^3 + … + 2^{50} + 2^{51}$
$\Rightarrow 2S – S = 2^{51} - 1$
$\Rightarrow S = 2^{51} - 1$
$\Rightarrow S < 2^{51}$
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Free Form | Lớp 9 | $ \left(x-2y\right)\sqrt{\frac{xy}{{\left(x-2y\right)}^{2}}}\left(x<2y<0\right)$ | $ x<2y<0\Rightarrow x-2y<0$
$ \left(x-2y\right)\sqrt{\frac{xy}{{\left(x-2y\right)}^{2}}}=\left(x-2y\right).\frac{\sqrt{xy}}{\left|x-2y\right|}=\left(x-2y\right).\frac{\sqrt{xy}}{-\left(x-2y\right)}=-\sqrt{xy}$ | https://khoahoc.vietjack.com/question/1008621 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><msqrt><mfrac><mrow><mi>x</mi><mi>y</mi></mrow><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt><mfenced><mrow><mi>x</mi><mo><</mo><mn>2</mn><mi>y</mi><mo><</mo><mn>0</mn></mrow></mfenced></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mn>2</mn><mi>y</mi><mo><</mo><mn>0</mn><mo>⇒</mo><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo><</mo><mn>0</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><msqrt><mfrac><mrow><mi>x</mi><mi>y</mi></mrow><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt><mo>=</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>.</mo><mfrac><msqrt><mi>x</mi><mi>y</mi></msqrt><mfenced close="|" open="|"><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced></mfrac><mo>=</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>.</mo><mfrac><msqrt><mi>x</mi><mi>y</mi></msqrt><mrow><mo>−</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced></mrow></mfrac><mo>=</mo><mo>−</mo><msqrt><mi>x</mi><mi>y</mi></msqrt></math>
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Free Form | Lớp 9 | Rút gọn các biểu thức sau :
$ \left(x-y\right)\sqrt{\frac{xy}{{\left(x-y\right)}^{2}}}$ | $ \begin{array}{l}\left(x-y\right)\sqrt{\frac{xy}{{\left(x-y\right)}^{2}}}=\left(x-y\right)\frac{\sqrt{xy}}{\sqrt{{\left(x-y\right)}^{2}}}\\ =\left(x-y\right).\frac{\sqrt{xy}}{\left|x-y\right|}=\left[\begin{array}{l}\sqrt{xy}(khi\text{\hspace{0.17em}}x-y>0)\\ -\sqrt{xy}\text{\hspace{0.17em}}(khi\text{\hspace{0.17em}}x-y<0)\end{array}\right.\end{array}$ | https://khoahoc.vietjack.com/question/1008625 | ### Câu hỏi:
Rút gọn các biểu thức sau :
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><msqrt><mfrac><mrow><mi>x</mi><mi>y</mi></mrow><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><msqrt><mfrac><mrow><mi>x</mi><mi>y</mi></mrow><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt><mo>=</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mfrac><msqrt><mi>x</mi><mi>y</mi></msqrt><msqrt><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mn>2</mn></msup></msqrt></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mo>.</mo><mfrac><msqrt><mi>x</mi><mi>y</mi></msqrt><mfenced close="|" open="|"><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced></mfrac><mo>=</mo><mfenced close="" open="["><mtable columnalign="left"><mtr><mtd><msqrt><mi>x</mi><mi>y</mi></msqrt><mo>(</mo><mi>k</mi><mi>h</mi><mi>i</mi><mtext> </mtext><mi>x</mi><mo>−</mo><mi>y</mi><mo>></mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mo>−</mo><msqrt><mi>x</mi><mi>y</mi></msqrt><mtext> </mtext><mo>(</mo><mi>k</mi><mi>h</mi><mi>i</mi><mtext> </mtext><mi>x</mi><mo>−</mo><mi>y</mi><mo><</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $ \sqrt{\frac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}}:\frac{2}{\sqrt{3}-1}$ | $ \begin{array}{l}\sqrt{\frac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}}:\frac{2}{\sqrt{3}-1}\\ =\sqrt{\frac{\sqrt{2}\left(2\sqrt{5}+\sqrt{15}-2-\sqrt{3}\right)}{\sqrt{2}\left(2\sqrt{5}-2\right)}}:\frac{2}{\sqrt{3}-1}\\ =\sqrt{\frac{\sqrt{5}\left(2+\sqrt{3}\right)-\left(2+\sqrt{3}\right)}{2\sqrt{5}-2}}.\frac{\sqrt{3}-1}{2}\\ =\sqrt{\frac{\left(2+\sqrt{3}\right)\left(\sqrt{5}-1\right)}{2\left(\sqrt{5}-1\right)}}.\frac{\sqrt{3}-1}{2}=\sqrt{\frac{2+\sqrt{3}}{2}}.\frac{\sqrt{3}-1}{2}\\ =\frac{\left(\sqrt{4+2\sqrt{3}}\right)\left(\sqrt{3}-1\right)}{2.2}=\frac{\sqrt{{\left(\sqrt{3}+1\right)}^{2}}.\left(\sqrt{3}-1\right)}{4}\\ =\frac{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}{4}=\frac{3-1}{4}=\frac{1}{2}\end{array}$ | https://khoahoc.vietjack.com/question/1008628 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>30</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac></msqrt><mo>:</mo><mfrac><mn>2</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mfrac><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>30</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac></msqrt><mo>:</mo><mfrac><mn>2</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mfrac><mrow><msqrt><mn>2</mn></msqrt><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><msqrt><mn>15</mn></msqrt><mo>−</mo><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><msqrt><mn>2</mn></msqrt><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></msqrt><mo>:</mo><mfrac><mn>2</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mfrac><mrow><msqrt><mn>5</mn></msqrt><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo>−</mo><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac></msqrt><mo>.</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mfrac><mrow><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></msqrt><mo>.</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt><mo>.</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mfenced><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></mfenced><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mn>2.2</mn></mfrac><mo>=</mo><mfrac><mrow><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mn>4</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>−</mo><mn>1</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | Đưa thừa số ra ngoài dấu căn:
$ \sqrt{275}$ | $ \sqrt{275}=\sqrt{25.11}=5\sqrt{11}$ | https://khoahoc.vietjack.com/question/1008629 | ### Câu hỏi:
Đưa thừa số ra ngoài dấu căn:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>275</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>275</mn></msqrt><mo>=</mo><msqrt><mn>25.11</mn></msqrt><mo>=</mo><mn>5</mn><msqrt><mn>11</mn></msqrt></math>
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Free Form | Lớp 9 | Đưa thừa số ra ngoài dấu căn:
$ 5\sqrt{70\text{\hspace{0.17em}}000}$ | $ 5\sqrt{70000}=5\sqrt{10000.7}=5.100\sqrt{7}=500\sqrt{7}$ | https://khoahoc.vietjack.com/question/1008630 | ### Câu hỏi:
Đưa thừa số ra ngoài dấu căn:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msqrt><mn>70</mn><mtext> </mtext><mn>000</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msqrt><mn>70000</mn></msqrt><mo>=</mo><mn>5</mn><msqrt><mn>10000.7</mn></msqrt><mo>=</mo><mn>5.100</mn><msqrt><mn>7</mn></msqrt><mo>=</mo><mn>500</mn><msqrt><mn>7</mn></msqrt></math>
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Free Form | Lớp 9 | Đưa thừa số ra ngoài dấu căn:
$ \sqrt{3{x}^{2}-12x+12}$ | $ \sqrt{3{x}^{2}-12x+12}=\sqrt{3.\left({x}^{2}-4x+4\right)}=\sqrt{3{\left(x-2\right)}^{2}}=\sqrt{3}.\left|x-2\right|$ | https://khoahoc.vietjack.com/question/1008631 | ### Câu hỏi:
Đưa thừa số ra ngoài dấu căn:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>12</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>12</mn></msqrt><mo>=</mo><msqrt><mn>3.</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mn>3</mn><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>3</mn></msqrt><mo>.</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>−</mo><mn>2</mn></mrow></mfenced></math>
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Free Form | Lớp 9 | Đưa thừa số ra ngoài dấu căn:
$ \sqrt{{x}^{4}-2{x}^{3}+3{x}^{2}-4x+2}$ | $ \begin{array}{l}\sqrt{{x}^{4}-2{x}^{3}+3{x}^{2}-4x+2}=\sqrt{\left({x}^{4}-2{x}^{3}+{x}^{2}\right)+\left(2{x}^{2}-4x+2\right)}\\ =\sqrt{{x}^{2}\left({x}^{2}-2x+1\right)+2\left({x}^{2}-2x+1\right)}=\sqrt{\left({x}^{2}-2x+1\right)\left({x}^{2}+2\right)}\\ =\sqrt{{\left(x-1\right)}^{2}\left({x}^{2}+2\right)}=\left|x-1\right|\sqrt{{x}^{2}+2}\end{array}$ | https://khoahoc.vietjack.com/question/1008636 | ### Câu hỏi:
Đưa thừa số ra ngoài dấu căn:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mi>x</mi><mn>4</mn></msup><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><msup><mi>x</mi><mn>4</mn></msup><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn></msqrt><mo>=</mo><msqrt><mfenced><mrow><msup><mi>x</mi><mn>4</mn></msup><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mi>x</mi><mn>2</mn></msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>2</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow></mfenced></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow></mfenced></msqrt><mo>=</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><msqrt><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></msqrt></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | <p>Tính</p>
<p>$ F=\sqrt{\frac{25+\sqrt{616}}{2}}-\sqrt{\frac{25-\sqrt{616}}{2}}$</p> | <p>$ \begin{array}{l}F=\sqrt{\frac{25+\sqrt{616}}{2}}-\sqrt{\frac{25-\sqrt{616}}{2}}=\frac{\sqrt{50+2\sqrt{616}}}{2}-\frac{\sqrt{50-2\sqrt{616}}}{2}\\ =\frac{\sqrt{{\left(\sqrt{28}\right)}^{2}+2.\sqrt{28}.\sqrt{22}+{\left(\sqrt{22}\right)}^{2}}-\sqrt{{\left(\sqrt{28}\right)}^{2}-2.\sqrt{28}.\sqrt{22}+{\left(\sqrt{22}\right)}^{2}}}{2}\\ =\frac{\sqrt{{\left(\sqrt{28}+\sqrt{22}\right)}^{2}}-\sqrt{{\left(\sqrt{28}-\sqrt{22}\right)}^{2}}}{2}=\frac{\sqrt{28}+\sqrt{22}-\sqrt{28}+\sqrt{22}}{2}=\sqrt{22}\end{array}$</p> | https://khoahoc.vietjack.com/question/1008640 | ### Câu hỏi:
<p>Tính</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><msqrt><mfrac><mrow><mn>25</mn><mo>+</mo><msqrt><mn>616</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt><mo>−</mo><msqrt><mfrac><mrow><mn>25</mn><mo>−</mo><msqrt><mn>616</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt></math></p>
### Lời giải:
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>F</mi><mo>=</mo><msqrt><mfrac><mrow><mn>25</mn><mo>+</mo><msqrt><mn>616</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt><mo>−</mo><msqrt><mfrac><mrow><mn>25</mn><mo>−</mo><msqrt><mn>616</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt><mo>=</mo><mfrac><msqrt><mn>50</mn><mo>+</mo><mn>2</mn><msqrt><mn>616</mn></msqrt></msqrt><mn>2</mn></mfrac><mo>−</mo><mfrac><msqrt><mn>50</mn><mo>−</mo><mn>2</mn><msqrt><mn>616</mn></msqrt></msqrt><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><msup><mfenced><msqrt><mn>28</mn></msqrt></mfenced><mn>2</mn></msup><mo>+</mo><mn>2.</mn><msqrt><mn>28</mn></msqrt><mo>.</mo><msqrt><mn>22</mn></msqrt><mo>+</mo><msup><mfenced><msqrt><mn>22</mn></msqrt></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><msqrt><msup><mfenced><msqrt><mn>28</mn></msqrt></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.</mn><msqrt><mn>28</mn></msqrt><mo>.</mo><msqrt><mn>22</mn></msqrt><mo>+</mo><msup><mfenced><msqrt><mn>22</mn></msqrt></mfenced><mn>2</mn></msup></msqrt></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><msup><mfenced><mrow><msqrt><mn>28</mn></msqrt><mo>+</mo><msqrt><mn>22</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>28</mn></msqrt><mo>−</mo><msqrt><mn>22</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>28</mn></msqrt><mo>+</mo><msqrt><mn>22</mn></msqrt><mo>−</mo><msqrt><mn>28</mn></msqrt><mo>+</mo><msqrt><mn>22</mn></msqrt></mrow><mn>2</mn></mfrac><mo>=</mo><msqrt><mn>22</mn></msqrt></mtd></mtr></mtable></math></p>
|
Free Form | Lớp 9 | <div><span>Giải phương trình:</span></div>
<div><span>$ \frac{2}{3}\sqrt{9x}-3\sqrt{4x}=\sqrt{25x}-16$</span></div> | <div>$ \begin{array}{l}\frac{2}{3}\sqrt{9x}-3\sqrt{4x}=\sqrt{25x}-16\left(x\ge 0\right)\\ \Leftrightarrow \frac{2}{3}.3\sqrt{x}-3.2\sqrt{x}-5\sqrt{x}=-16\\ \Leftrightarrow -9\sqrt{x}=-16\Leftrightarrow \sqrt{x}=\frac{16}{9}\\ \Rightarrow x=\frac{256}{81}\left(tm\right)\end{array}$</div> | https://khoahoc.vietjack.com/question/1008643 | ### Câu hỏi:
<div><span>Giải phương trình:</span></div>
<div><span><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>4</mn><mi>x</mi></msqrt><mo>=</mo><msqrt><mn>25</mn><mi>x</mi></msqrt><mo>−</mo><mn>16</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo></math></span></div>
### Lời giải:
<div><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mn>2</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>4</mn><mi>x</mi></msqrt><mo>=</mo><msqrt><mn>25</mn><mi>x</mi></msqrt><mo>−</mo><mn>16</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mn>0</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mn>.3</mn><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>3.2</mn><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>5</mn><msqrt><mi>x</mi></msqrt><mo>=</mo><mo>−</mo><mn>16</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mo>−</mo><mn>9</mn><msqrt><mi>x</mi></msqrt><mo>=</mo><mo>−</mo><mn>16</mn><mo>⇔</mo><msqrt><mi>x</mi></msqrt><mo>=</mo><mfrac><mn>16</mn><mn>9</mn></mfrac></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mn>256</mn><mn>81</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math></div>
|
Free Form | Lớp 9 | Giải phương trình:
$ 4\sqrt{x+5}=16$ | $ \begin{array}{l}4\sqrt{x+5}=16\\ \Leftrightarrow \sqrt{x+5}=4\left(x\ge -5\right)\\ \Rightarrow x+5=16\Leftrightarrow x=11\left(tm\right)\end{array}$ | https://khoahoc.vietjack.com/question/1008647 | ### Câu hỏi:
Giải phương trình:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>16</mn></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mn>4</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>16</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>4</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mo>−</mo><mn>5</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>16</mn><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>11</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ \sqrt{4{x}^{2}-4x+1}=1-x$ | $ \begin{array}{l}\sqrt{4{x}^{2}-4x+1}=1-x\left(x\le 1\right)\\ \Leftrightarrow 4{x}^{2}-4x+1=1-2x+{x}^{2}\\ \Leftrightarrow 3{x}^{2}-2x=0\Leftrightarrow x\left(3x-2\right)=0\\ \Leftrightarrow \left[\begin{array}{l}x=0\left(tm\right)\\ x=\frac{2}{3}\left(tm\right)\end{array}\right.\end{array}\frac{}{}$ | https://khoahoc.vietjack.com/question/1008650 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><mn>1</mn><mo>−</mo><mi>x</mi></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><mn>1</mn><mo>−</mo><mi>x</mi><mfenced><mrow><mi>x</mi><mo>≤</mo><mn>1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>1</mn><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>=</mo><mn>0</mn><mo>⇔</mo><mi>x</mi><mfenced><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mfenced close="" open="["><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>0</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><mfrac><mrow></mrow><mrow></mrow></mfrac></math>
|
Free Form | Lớp 9 | $ \sqrt{4x-12}+\frac{1}{3}\sqrt{9x-27}-4=\frac{1}{2}\sqrt{16x-48}$ | $ \begin{array}{l}\sqrt{4x-12}+\frac{1}{3}\sqrt{9x-27}-4=\frac{1}{2}\sqrt{16x-48}\\ \Leftrightarrow \sqrt{4(x-3)}+\frac{1}{3}\sqrt{9\left(x-3\right)}-\frac{1}{2}\sqrt{16\left(x-3\right)}=4\\ \Leftrightarrow 2\sqrt{x-3}+\sqrt{x-3}-2\sqrt{x-3}=4\left(x\ge 3\right)\\ \Leftrightarrow \sqrt{x-3}=4\Rightarrow x-3=16\Leftrightarrow x=19\left(tm\right)\end{array}$ | https://khoahoc.vietjack.com/question/1008651 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>4</mn><mi>x</mi><mo>−</mo><mn>12</mn></msqrt><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi><mo>−</mo><mn>27</mn></msqrt><mo>−</mo><mn>4</mn><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>16</mn><mi>x</mi><mo>−</mo><mn>48</mn></msqrt><mo> </mo></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>4</mn><mi>x</mi><mo>−</mo><mn>12</mn></msqrt><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi><mo>−</mo><mn>27</mn></msqrt><mo>−</mo><mn>4</mn><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>16</mn><mi>x</mi><mo>−</mo><mn>48</mn></msqrt></mtd></mtr><mtr><mtd><mo>⇔</mo><msqrt><mn>4</mn><mo>(</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo>)</mo></msqrt><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mfenced><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>16</mn><mfenced><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msqrt><mi>x</mi><mo>−</mo><mn>3</mn></msqrt><mo>+</mo><msqrt><mi>x</mi><mo>−</mo><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mi>x</mi><mo>−</mo><mn>3</mn></msqrt><mo>=</mo><mn>4</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mn>3</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><msqrt><mi>x</mi><mo>−</mo><mn>3</mn></msqrt><mo>=</mo><mn>4</mn><mo>⇒</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo>=</mo><mn>16</mn><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>19</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ \sqrt{4x+20}-3\sqrt{5+x}+\frac{4}{3}\sqrt{9x+45}=6$ | $ \begin{array}{l}\sqrt{4x+20}-3\sqrt{5+x}+\frac{4}{3}\sqrt{9x+45}=6\\ \Leftrightarrow 2\sqrt{x+5}-3\sqrt{x+5}+\frac{4}{3}\mathrm{.3.}\sqrt{x+5}=6\left(x\ge -5\right)\\ \Leftrightarrow -\sqrt{x+5}+4\sqrt{x+5}=6\\ \Leftrightarrow 3\sqrt{x+5}=6\Leftrightarrow \sqrt{x+5}=2\\ \Rightarrow x+5=4\Leftrightarrow x=-1\left(tm\right)\end{array}\frac{}{}$ | https://khoahoc.vietjack.com/question/1008657 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>4</mn><mi>x</mi><mo>+</mo><mn>20</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>5</mn><mo>+</mo><mi>x</mi></msqrt><mo>+</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi><mo>+</mo><mn>45</mn></msqrt><mo>=</mo><mn>6</mn></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>4</mn><mi>x</mi><mo>+</mo><mn>20</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>5</mn><mo>+</mo><mi>x</mi></msqrt><mo>+</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi><mo>+</mo><mn>45</mn></msqrt><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>+</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mn>.3.</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>6</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mo>−</mo><mn>5</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><mo>−</mo><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>+</mo><mn>4</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>3</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>6</mn><mo>⇔</mo><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>4</mn><mo>⇔</mo><mi>x</mi><mo>=</mo><mo>−</mo><mn>1</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable><mfrac><mrow></mrow><mrow></mrow></mfrac></math>
|
Free Form | Lớp 9 | <p>Rút gọn </p>
<p>$ \frac{2}{2a-1}.\sqrt{5{a}^{4}\left(1-4a+4{a}^{2}\right)}$</p> | $ \begin{array}{l}\frac{2}{2a-1}\sqrt{5{a}^{4}\left(1-4a+4{a}^{2}\right)}=\frac{2}{2a-1}.\sqrt{5}.{a}^{2}.\left|1-2a\right|\\ =\left[\begin{array}{l}-2{a}^{2}\sqrt{5}(Khi\text{\hspace{0.17em}}1-2a>0)\\ 2{a}^{2}\sqrt{5}\text{\hspace{0.17em}}(khi\text{\hspace{0.17em}}1-2a<0)\end{array}\right.\end{array}$ | https://khoahoc.vietjack.com/question/1008660 | ### Câu hỏi:
<p>Rút gọn </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mrow><mn>2</mn><mi>a</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>.</mo><msqrt><mn>5</mn><msup><mi>a</mi><mn>4</mn></msup><mfenced><mrow><mn>1</mn><mo>−</mo><mn>4</mn><mi>a</mi><mo>+</mo><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfenced></msqrt></math></p>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mn>2</mn><mrow><mn>2</mn><mi>a</mi><mo>−</mo><mn>1</mn></mrow></mfrac><msqrt><mn>5</mn><msup><mi>a</mi><mn>4</mn></msup><mfenced><mrow><mn>1</mn><mo>−</mo><mn>4</mn><mi>a</mi><mo>+</mo><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfenced></msqrt><mo>=</mo><mfrac><mn>2</mn><mrow><mn>2</mn><mi>a</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>.</mo><msqrt><mn>5</mn></msqrt><mo>.</mo><msup><mi>a</mi><mn>2</mn></msup><mo>.</mo><mfenced close="|" open="|"><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>a</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced close="" open="["><mtable columnalign="left"><mtr><mtd><mo>−</mo><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><msqrt><mn>5</mn></msqrt><mo>(</mo><mi>K</mi><mi>h</mi><mi>i</mi><mtext> </mtext><mn>1</mn><mo>−</mo><mn>2</mn><mi>a</mi><mo>></mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><msqrt><mn>5</mn></msqrt><mtext> </mtext><mo>(</mo><mi>k</mi><mi>h</mi><mi>i</mi><mtext> </mtext><mn>1</mn><mo>−</mo><mn>2</mn><mi>a</mi><mo><</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | Rút gọn
$ \left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right):\left(a-b\right)+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}$ | $ \begin{array}{l}\left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right):\left(a-b\right)+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ =\left[\frac{{\sqrt{a}}^{3}+{\sqrt{b}}^{3}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right]:\left(a-b\right)+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ =\left[\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right].\frac{1}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ =\left(a-2\sqrt{ab}+b\right).\frac{1}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ ={\left(\sqrt{a}-\sqrt{b}\right)}^{2}.\frac{1}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ =\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}\text{\hspace{0.17em}}}=1\end{array}$ | https://khoahoc.vietjack.com/question/1008667 | ### Câu hỏi:
Rút gọn
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mi>a</mi><msqrt><mi>a</mi></msqrt><mo>+</mo><mi>b</mi><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow></mfenced><mo>:</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mi>b</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mfrac><mrow><mi>a</mi><msqrt><mi>a</mi></msqrt><mo>+</mo><mi>b</mi><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow></mfenced><mo>:</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mi>b</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><msup><msqrt><mi>a</mi></msqrt><mn>3</mn></msup><mo>+</mo><msup><msqrt><mi>b</mi></msqrt><mn>3</mn></msup></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow></mfenced><mo>:</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mi>b</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mfenced><mrow><mi>a</mi><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mi>b</mi></mrow></mfenced></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow></mfenced><mo>.</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mn>2</mn><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mi>b</mi></mrow></mfenced><mo>.</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msup><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mn>2</mn></msup><mo>.</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt><mtext> </mtext></mrow></mfrac><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math>
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Free Form | Lớp 7 | Cho biết $x$ và $y$ là hai đại lượng tỉ lệ thuận với nhau và khi $x=3$ thì $y=-2,7$. Tìm hệ số tỉ lệ $k$ của $y$ đối với $x$ và biểu diễn $y$ theo $x$. | $x$ và $y$ là hai đại lượng tỉ lệ thuận với nhau nên $y=kx$. $(k\neq 0)$
Khi $x=3$ thì $y=-2,7$ ta có: $-2,7=k.3\Rightarrow k=-0,9$
Vậy hệ số tỉ lệ $k$ của $y$ đối với $x$ là: $-0,9$. Biểu diễn $y$ theo $x$ là: $y=-0,9.x$ | https://khoahoc.vietjack.com/question/1008671 | ### Câu hỏi:
Cho biết $x$ và $y$ là hai đại lượng tỉ lệ thuận với nhau và khi $x=3$ thì $y=-2,7$. Tìm hệ số tỉ lệ $k$ của $y$ đối với $x$ và biểu diễn $y$ theo $x$.
### Lời giải:
$x$ và $y$ là hai đại lượng tỉ lệ thuận với nhau nên $y=kx$. $(k\neq 0)$
Khi $x=3$ thì $y=-2,7$ ta có: $-2,7=k.3\Rightarrow k=-0,9$
Vậy hệ số tỉ lệ $k$ của $y$ đối với $x$ là: $-0,9$. Biểu diễn $y$ theo $x$ là: $y=-0,9.x$
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Free Form | Lớp 7 | Cho biết x và y là hai đại lượng tỉ lệ thuận với nhau và khi $x=3$ thì $y=-2,7$. Tính giá trị của y khi x=2 và tính giá trị của x khi y=0,9. | * Khi $x=-2$ thay vào biểu thức $y=-0,9x$ ta có:
$y = -0,9.(-2)=1,8$, vậy khi $x=-2$ thì $y=1,8$
* Khi $y=0,9$ thay vào biểu thức $y=-0,9x$ ta có:
$0,9=-0,9x \Rightarrow x=-1.$ Vậy khi $y=0,9$ thì $x=-1$ | https://khoahoc.vietjack.com/question/1008681 | ### Câu hỏi:
Cho biết x và y là hai đại lượng tỉ lệ thuận với nhau và khi $x=3$ thì $y=-2,7$. Tính giá trị của y khi x=2 và tính giá trị của x khi y=0,9.
### Lời giải:
* Khi $x=-2$ thay vào biểu thức $y=-0,9x$ ta có:
$y = -0,9.(-2)=1,8$, vậy khi $x=-2$ thì $y=1,8$
* Khi $y=0,9$ thay vào biểu thức $y=-0,9x$ ta có:
$0,9=-0,9x \Rightarrow x=-1.$ Vậy khi $y=0,9$ thì $x=-1$
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Free Form | Lớp 9 | Rút gọn biểu thức :
$ \frac{5}{12\left(2\sqrt{5}+3\sqrt{2}\right)}-\frac{5}{12\left(2\sqrt{5}-3\sqrt{2}\right)}$ | $ \begin{array}{l}\frac{5}{12\left(2\sqrt{5}+3\sqrt{2}\right)}-\frac{5}{12\left(2\sqrt{5}-3\sqrt{2}\right)}\\ =\frac{5\left(2\sqrt{5}-3\sqrt{2}\right)-5\left(2\sqrt{5}+3\sqrt{2}\right)}{12\left(2\sqrt{5}+3\sqrt{2}\right)\left(2\sqrt{5}-3\sqrt{2}\right)}\\ =\frac{10\sqrt{5}-15\sqrt{2}-10\sqrt{5}-15\sqrt{2}}{12\left(20-18\right)}=\frac{-30\sqrt{2}}{24}=\frac{-5\sqrt{2}}{4}\end{array}$ | https://khoahoc.vietjack.com/question/1008684 | ### Câu hỏi:
Rút gọn biểu thức :
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac><mo>−</mo><mfrac><mn>5</mn><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mn>5</mn><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac><mo>−</mo><mfrac><mn>5</mn><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>5</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced><mo>−</mo><mn>5</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>10</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>15</mn><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>10</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>15</mn><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>12</mn><mfenced><mrow><mn>20</mn><mo>−</mo><mn>18</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>30</mn><msqrt><mn>2</mn></msqrt></mrow><mn>24</mn></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>5</mn><msqrt><mn>2</mn></msqrt></mrow><mn>4</mn></mfrac></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}$ | $\begin{aligned}
\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}} &= \frac{\sqrt{5}.(\sqrt{5}+1)}{\sqrt{5}.(\sqrt{5}-1)}+\frac{\sqrt{5}.(\sqrt{5}-1)}{\sqrt{5}.(\sqrt{5}+1)} \\
&= \frac{\sqrt{5}+1}{\sqrt{5}-1}+\frac{\sqrt{5}-1}{\sqrt{5}+1} = \frac{(\sqrt{5}+1)^2+(\sqrt{5}-1)^2}{(\sqrt{5}-1)(\sqrt{5}+1)} \\
&= \frac{6+2\sqrt{5}+6-2\sqrt{5}}{5-1} = \frac{12}{4} = 3
\end{aligned}$ | https://khoahoc.vietjack.com/question/1008687 | ### Câu hỏi:
$\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}$
### Lời giải:
$\begin{aligned}
\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}} &= \frac{\sqrt{5}.(\sqrt{5}+1)}{\sqrt{5}.(\sqrt{5}-1)}+\frac{\sqrt{5}.(\sqrt{5}-1)}{\sqrt{5}.(\sqrt{5}+1)} \\
&= \frac{\sqrt{5}+1}{\sqrt{5}-1}+\frac{\sqrt{5}-1}{\sqrt{5}+1} = \frac{(\sqrt{5}+1)^2+(\sqrt{5}-1)^2}{(\sqrt{5}-1)(\sqrt{5}+1)} \\
&= \frac{6+2\sqrt{5}+6-2\sqrt{5}}{5-1} = \frac{12}{4} = 3
\end{aligned}$
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Free Form | Lớp 9 | $ \frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}$ | $ \begin{array}{l}\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}\\ =\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}+1\right)-\sqrt{3}\left(\sqrt{\sqrt{3}+1}-1\right)}{\sqrt{{\left(\sqrt{3}+1\right)}^{2}}-1}\\ =\frac{\sqrt{3}.\left[\sqrt{\sqrt{3}+1}+1-\sqrt{\sqrt{3}+1}+1\right]}{\sqrt{3}+1-1}\\ =\sqrt{\sqrt{3}+1}+1-\sqrt{\sqrt{3}+1}+1=2\end{array}$ | https://khoahoc.vietjack.com/question/1008713 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><msqrt><mn>3</mn></msqrt><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mo>−</mo><msqrt><mn>3</mn></msqrt><mfenced><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>.</mo><mfenced close="]" open="["><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn><mo>=</mo><mn>2</mn></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $ \sqrt{\frac{16{x}^{3}}{81y}}$ | $ \sqrt{\frac{16{x}^{3}}{81y}}=\sqrt{\frac{16}{81}}.\frac{\sqrt{{x}^{3}}}{\sqrt{y}}=\frac{4x\sqrt{x}}{9\sqrt{y}}=\frac{4x\sqrt{xy}}{9y}$ | https://khoahoc.vietjack.com/question/1008891 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mrow><mn>81</mn><mi>y</mi></mrow></mfrac></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mrow><mn>81</mn><mi>y</mi></mrow></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mn>16</mn><mn>81</mn></mfrac></msqrt><mo>.</mo><mfrac><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><msqrt><mi>y</mi></msqrt></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow><mrow><mn>9</mn><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><msqrt><mi>x</mi><mi>y</mi></msqrt></mrow><mrow><mn>9</mn><mi>y</mi></mrow></mfrac></math>
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Free Form | Lớp 9 | $ \sqrt{\frac{16{x}^{3}}{81y}}$ | $ \sqrt{\frac{16{x}^{3}}{81y}}=\sqrt{\frac{16}{81}}.\frac{\sqrt{{x}^{3}}}{\sqrt{y}}=\frac{4x\sqrt{x}}{9\sqrt{y}}=\frac{4x\sqrt{xy}}{9y}$ | https://khoahoc.vietjack.com/question/1008892 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mrow><mn>81</mn><mi>y</mi></mrow></mfrac></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mrow><mn>81</mn><mi>y</mi></mrow></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mn>16</mn><mn>81</mn></mfrac></msqrt><mo>.</mo><mfrac><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><msqrt><mi>y</mi></msqrt></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow><mrow><mn>9</mn><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><msqrt><mi>x</mi><mi>y</mi></msqrt></mrow><mrow><mn>9</mn><mi>y</mi></mrow></mfrac></math>
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Free Form | Lớp 9 | $\frac{15}{\sqrt{7}-2}$ | $\begin{aligned}
\frac{15}{\sqrt{7}-2} &= \frac{15(\sqrt{7}+2)}{7-4} = \frac{15(\sqrt{7}+2)}{3} = 5(\sqrt{7}+2) \\
&= 5\sqrt{7}+10
\end{aligned}$ | https://khoahoc.vietjack.com/question/1008899 | ### Câu hỏi:
$\frac{15}{\sqrt{7}-2}$
### Lời giải:
$\begin{aligned}
\frac{15}{\sqrt{7}-2} &= \frac{15(\sqrt{7}+2)}{7-4} = \frac{15(\sqrt{7}+2)}{3} = 5(\sqrt{7}+2) \\
&= 5\sqrt{7}+10
\end{aligned}$
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Free Form | Lớp 9 | $ \frac{3\sqrt{3}+3}{2\sqrt{3}}$ | $ \frac{3\sqrt{3}+3}{2\sqrt{3}}=\frac{\sqrt{3}.\left(3+\sqrt{3}\right)}{2\sqrt{3}}=\frac{3+\sqrt{3}}{2}$ | https://khoahoc.vietjack.com/question/1008902 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>3</mn></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>3</mn></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>.</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac></math>
|
Free Form | Lớp 9 | Trục căn thức ở mẫu:
$ \frac{2\sqrt{3}-\sqrt{6}}{\sqrt{2}-1}$ | $ \frac{2\sqrt{3}-\sqrt{6}}{\sqrt{2}-1}=\frac{\sqrt{6}.\left(\sqrt{2}-1\right)}{\sqrt{2}-1}=\sqrt{6}$ | https://khoahoc.vietjack.com/question/1008904 | ### Câu hỏi:
Trục căn thức ở mẫu:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>6</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>=</mo><msqrt><mn>6</mn></msqrt></math>
|
Free Form | Lớp 9 | $ B=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\mathrm{........}+\frac{1}{\sqrt{2005}+\sqrt{2006}}$ | $ \begin{array}{l}B=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\mathrm{.....}+\frac{1}{\sqrt{2004}+\sqrt{2005}}\\ =\frac{\sqrt{2}-1}{2-1}+\frac{\sqrt{3}-\sqrt{2}}{3-2}+\frac{\sqrt{4}-\sqrt{3}}{4-3}+\mathrm{......}+\frac{\sqrt{2006}-\sqrt{2005}}{2006-2005}\\ =\sqrt{2}-1+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\mathrm{...}+\sqrt{2006}-\sqrt{2005}\\ =\sqrt{2006}-1\\ \end{array}$ | https://khoahoc.vietjack.com/question/1008910 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mn>........</mn><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2005</mn></msqrt><mo>+</mo><msqrt><mn>2006</mn></msqrt></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>B</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>4</mn></msqrt></mrow></mfrac><mo>+</mo><mn>.....</mn><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2004</mn></msqrt><mo>+</mo><msqrt><mn>2005</mn></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>−</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>3</mn><mo>−</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>4</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>4</mn><mo>−</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mn>......</mn><mo>+</mo><mfrac><mrow><msqrt><mn>2006</mn></msqrt><mo>−</mo><msqrt><mn>2005</mn></msqrt></mrow><mrow><mn>2006</mn><mo>−</mo><mn>2005</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>4</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>...</mn><mo>+</mo><msqrt><mn>2006</mn></msqrt><mo>−</mo><msqrt><mn>2005</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>2006</mn></msqrt><mo>−</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ C=\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\mathrm{........}-\frac{1}{\sqrt{48}-\sqrt{49}}$ | $ \begin{array}{l}C=\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\mathrm{.......}-\frac{1}{\sqrt{48}-\sqrt{49}}\\ =\frac{\sqrt{1}+\sqrt{2}}{1-2}-\frac{\sqrt{2}+\sqrt{3}}{2-3}+\frac{\sqrt{3}-\sqrt{4}}{3-4}-\mathrm{.....}-\frac{\sqrt{48}+\sqrt{49}}{48-49}\\ =-1-\sqrt{2}+\sqrt{2}+\sqrt{3}-\sqrt{3}-\sqrt{4}-\mathrm{.....}+\sqrt{48}+\sqrt{49}\\ =-1+\sqrt{49}=-1+7=6\end{array}$ | https://khoahoc.vietjack.com/question/1008911 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mn>1</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>4</mn></msqrt></mrow></mfrac><mo>−</mo><mn>........</mn><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mn>48</mn></msqrt><mo>−</mo><msqrt><mn>49</mn></msqrt></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mn>1</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>4</mn></msqrt></mrow></mfrac><mo>−</mo><mn>.......</mn><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mn>48</mn></msqrt><mo>−</mo><msqrt><mn>49</mn></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>1</mn></msqrt><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>−</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>4</mn></msqrt></mrow><mrow><mn>3</mn><mo>−</mo><mn>4</mn></mrow></mfrac><mo>−</mo><mn>.....</mn><mo>−</mo><mfrac><mrow><msqrt><mn>48</mn></msqrt><mo>+</mo><msqrt><mn>49</mn></msqrt></mrow><mrow><mn>48</mn><mo>−</mo><mn>49</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mo>−</mo><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>4</mn></msqrt><mo>−</mo><mn>.....</mn><mo>+</mo><msqrt><mn>48</mn></msqrt><mo>+</mo><msqrt><mn>49</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mo>−</mo><mn>1</mn><mo>+</mo><msqrt><mn>49</mn></msqrt><mo>=</mo><mo>−</mo><mn>1</mn><mo>+</mo><mn>7</mn><mo>=</mo><mn>6</mn></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ D=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\mathrm{......}+\frac{1}{100\sqrt{99}+99\sqrt{100}}$ | <p>
$ \begin{array}{l}\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n\left(n+1\right)}\left(\sqrt{n+1}+\sqrt{n}\right)}\\ =\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n\left(n+1\right)}.\left(\sqrt{n+1}+\sqrt{n}\right)}=\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n\left(n+1\right)}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n}+1}\end{array}$
</p>
<p>
$ D=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+\mathrm{.....}+\frac{1}{\sqrt{99}}-\frac{1}{\sqrt{100}}=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{100}}=\frac{9}{10}$
</p> | https://khoahoc.vietjack.com/question/1008917 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><msqrt><mn>1</mn></msqrt><mo>+</mo><mn>1</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mn>......</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>100</mn><msqrt><mn>99</mn></msqrt><mo>+</mo><mn>99</mn><msqrt><mn>100</mn></msqrt></mrow></mfrac></math>
### Lời giải:
<p>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced><msqrt><mi>n</mi></msqrt><mo>+</mo><mi>n</mi><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mi>n</mi><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt><mfenced><mrow><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><msqrt><mi>n</mi></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><msqrt><mi>n</mi></msqrt></mrow><mrow><msqrt><mi>n</mi><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt><mo>.</mo><mfenced><mrow><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><msqrt><mi>n</mi></msqrt></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><msqrt><mi>n</mi></msqrt></mrow><msqrt><mi>n</mi><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt></mfrac><mo>=</mo><mfrac><mn>1</mn><msqrt><mi>n</mi></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mi>n</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></mtd></mtr></mtable></math>
</p>
<p>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>1</mn></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mo>+</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><msqrt><mn>3</mn></msqrt></mfrac><mo>+</mo><mn>.....</mn><mo>+</mo><mfrac><mn>1</mn><msqrt><mn>99</mn></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><msqrt><mn>100</mn></msqrt></mfrac><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>1</mn></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><msqrt><mn>100</mn></msqrt></mfrac><mo>=</mo><mfrac><mn>9</mn><mn>10</mn></mfrac></math>
</p>
|
Free Form | Lớp 9 | Rút gọn biểu thức:
$ \frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}$ | $ \frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\frac{{\sqrt{x}}^{3}-{\sqrt{y}}^{3}}{\sqrt{x}-\sqrt{y}}=\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\sqrt{x}-\sqrt{y}}=x+\sqrt{xy}+y$ | https://khoahoc.vietjack.com/question/1008921 | ### Câu hỏi:
Rút gọn biểu thức:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mi>y</mi><msqrt><mi>y</mi></msqrt></mrow><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mi>y</mi><msqrt><mi>y</mi></msqrt></mrow><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><msqrt><mi>x</mi></msqrt><mn>3</mn></msup><mo>−</mo><msup><msqrt><mi>y</mi></msqrt><mn>3</mn></msup></mrow><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi><mi>y</mi></msqrt><mo>+</mo><mi>y</mi></mrow></mfenced></mrow><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><msqrt><mi>x</mi><mi>y</mi></msqrt><mo>+</mo><mi>y</mi></math>
|
Free Form | Lớp 9 | Rút gọn biểu thức:
$$\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt{3}}$$ | $$\begin{aligned}
&\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt{3}}=\frac{x-\sqrt{3x}+3}{(\sqrt{x}+\sqrt{3})(x-\sqrt{3x}+3)}=\frac{1}{\sqrt{x}+\sqrt{3}}=\frac{x-\sqrt{3}}{x-3}
\end{aligned}$$ | https://khoahoc.vietjack.com/question/1008926 | ### Câu hỏi:
Rút gọn biểu thức:
$$\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt{3}}$$
### Lời giải:
$$\begin{aligned}
&\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt{3}}=\frac{x-\sqrt{3x}+3}{(\sqrt{x}+\sqrt{3})(x-\sqrt{3x}+3)}=\frac{1}{\sqrt{x}+\sqrt{3}}=\frac{x-\sqrt{3}}{x-3}
\end{aligned}$$
|
Free Form | Lớp 9 | $ \sqrt{10+\sqrt{3}x}=2+\sqrt{6}$ | $ \begin{array}{l}\sqrt{10+\sqrt{3x}}=2+\sqrt{6}\left(x\ge 0\right)\\ \Rightarrow 10+\sqrt{3x}=10+4\sqrt{6}\\ \sqrt{3x}=4\sqrt{6}\Rightarrow 3x=96\Leftrightarrow x=32\left(tm\right)\end{array}$ | https://khoahoc.vietjack.com/question/1008931 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>10</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mi>x</mi></msqrt><mo>=</mo><mn>2</mn><mo>+</mo><msqrt><mn>6</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>10</mn><mo>+</mo><msqrt><mn>3</mn><mi>x</mi></msqrt></msqrt><mo>=</mo><mn>2</mn><mo>+</mo><msqrt><mn>6</mn></msqrt><mfenced><mrow><mi>x</mi><mo>≥</mo><mn>0</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇒</mo><mn>10</mn><mo>+</mo><msqrt><mn>3</mn><mi>x</mi></msqrt><mo>=</mo><mn>10</mn><mo>+</mo><mn>4</mn><msqrt><mn>6</mn></msqrt></mtd></mtr><mtr><mtd><msqrt><mn>3</mn><mi>x</mi></msqrt><mo>=</mo><mn>4</mn><msqrt><mn>6</mn></msqrt><mo>⇒</mo><mn>3</mn><mi>x</mi><mo>=</mo><mn>96</mn><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>32</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | Tìm x biết:
$\sqrt{3x-2}=2-\sqrt{3}$ | $\begin{aligned}
\sqrt{3x-2}&=2-\sqrt{3} \left(x\geq \frac{2}{3}\right)\\
\Rightarrow 3x-2&=7-4\sqrt{3}\\
\Leftrightarrow 3x&=9-4\sqrt{3}\Rightarrow x=3-\frac{4}{3}\sqrt{3} \left(tm\right)
\end{aligned}$ | https://khoahoc.vietjack.com/question/1008932 | ### Câu hỏi:
Tìm x biết:
$\sqrt{3x-2}=2-\sqrt{3}$
### Lời giải:
$\begin{aligned}
\sqrt{3x-2}&=2-\sqrt{3} \left(x\geq \frac{2}{3}\right)\\
\Rightarrow 3x-2&=7-4\sqrt{3}\\
\Leftrightarrow 3x&=9-4\sqrt{3}\Rightarrow x=3-\frac{4}{3}\sqrt{3} \left(tm\right)
\end{aligned}$
|
Free Form | Lớp 9 | Tìm x biết:
$\sqrt{x+1}=\sqrt{5}-3$ | $\begin{aligned}
&\sqrt{x+1}=\sqrt{5}-3(x\geq -1)\\
&\Rightarrow x+1=14-6\sqrt{5}\\
&\Rightarrow x=13-6\sqrt{5}(tm)
\end{aligned}$ | https://khoahoc.vietjack.com/question/1008935 | ### Câu hỏi:
Tìm x biết:
$\sqrt{x+1}=\sqrt{5}-3$
### Lời giải:
$\begin{aligned}
&\sqrt{x+1}=\sqrt{5}-3(x\geq -1)\\
&\Rightarrow x+1=14-6\sqrt{5}\\
&\Rightarrow x=13-6\sqrt{5}(tm)
\end{aligned}$
|
Free Form | Lớp 9 | $\frac{2}{\sqrt{6}-2}-\frac{4}{3-\sqrt{5}}$ | $\frac{2}{\sqrt{6}-2}-\frac{4}{3-\sqrt{5}}=\frac{2(\sqrt{6}+2)}{6-4}-\frac{4(3+\sqrt{5})}{9-5}=\sqrt{6}+2-3-\sqrt{5}=\sqrt{6}-\sqrt{5}-1$ | https://khoahoc.vietjack.com/question/1008955 | ### Câu hỏi:
$\frac{2}{\sqrt{6}-2}-\frac{4}{3-\sqrt{5}}$
### Lời giải:
$\frac{2}{\sqrt{6}-2}-\frac{4}{3-\sqrt{5}}=\frac{2(\sqrt{6}+2)}{6-4}-\frac{4(3+\sqrt{5})}{9-5}=\sqrt{6}+2-3-\sqrt{5}=\sqrt{6}-\sqrt{5}-1$
|
Free Form | Lớp 9 | $ \sqrt{96}-6\sqrt{\frac{2}{3}}+\frac{3}{3+\sqrt{6}}-\sqrt{10-4\sqrt{6}}$ | $ \begin{array}{l}\sqrt{96}-6\sqrt{\frac{2}{3}}+\frac{3}{3+\sqrt{6}}-\sqrt{10-4\sqrt{6}}\\ =\sqrt{16.6}-\frac{6\sqrt{2}}{\sqrt{3}}+\frac{3\left(3-\sqrt{6}\right)}{9-6}-\sqrt{{\left(\sqrt{6}\right)}^{2}-2.\sqrt{6}.2+{2}^{2}}\\ =4\sqrt{6}-2\sqrt{6}+3-\sqrt{6}-\sqrt{{\left(\sqrt{6}-2\right)}^{2}}\\ =\sqrt{6}+3-\left|\sqrt{6}-2\right|=\sqrt{6}+3-\sqrt{6}+2=5\end{array}$ | https://khoahoc.vietjack.com/question/1008959 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>96</mn></msqrt><mo>−</mo><mn>6</mn><msqrt><mfrac><mn>2</mn><mn>3</mn></mfrac></msqrt><mo>+</mo><mfrac><mn>3</mn><mrow><mn>3</mn><mo>+</mo><msqrt><mn>6</mn></msqrt></mrow></mfrac><mo>−</mo><msqrt><mn>10</mn><mo>−</mo><mn>4</mn><msqrt><mn>6</mn></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>96</mn></msqrt><mo>−</mo><mn>6</mn><msqrt><mfrac><mn>2</mn><mn>3</mn></mfrac></msqrt><mo>+</mo><mfrac><mn>3</mn><mrow><mn>3</mn><mo>+</mo><msqrt><mn>6</mn></msqrt></mrow></mfrac><mo>−</mo><msqrt><mn>10</mn><mo>−</mo><mn>4</mn><msqrt><mn>6</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>16.6</mn></msqrt><mo>−</mo><mfrac><mrow><mn>6</mn><msqrt><mn>2</mn></msqrt></mrow><msqrt><mn>3</mn></msqrt></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mn>3</mn><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow></mfenced></mrow><mrow><mn>9</mn><mo>−</mo><mn>6</mn></mrow></mfrac><mo>−</mo><msqrt><msup><mfenced><msqrt><mn>6</mn></msqrt></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.</mn><msqrt><mn>6</mn></msqrt><mn>.2</mn><mo>+</mo><msup><mn>2</mn><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>4</mn><msqrt><mn>6</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>3</mn><mo>−</mo><msqrt><mn>6</mn></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>6</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>3</mn><mo>−</mo><mfenced close="|" open="|"><mrow><msqrt><mn>6</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mo>=</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>3</mn><mo>−</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>2</mn><mo>=</mo><mn>5</mn></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $ \sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}$ | $ \begin{array}{l}\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\\ =\frac{\sqrt{4+2\sqrt{3}}}{\sqrt{2}}+\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}=\frac{\sqrt{{\left(\sqrt{3}+1\right)}^{2}}}{\sqrt{2}}+\frac{\sqrt{{\left(\sqrt{3}-1\right)}^{2}}}{\sqrt{2}}\\ =\frac{\sqrt{3}+1+\sqrt{3}-1}{\sqrt{2}}=\frac{2\sqrt{3}}{\sqrt{2}}=\sqrt{6}\end{array}$ | https://khoahoc.vietjack.com/question/1008966 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt><msqrt><mn>2</mn></msqrt></mfrac><mo>+</mo><mfrac><msqrt><mn>4</mn><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt><msqrt><mn>2</mn></msqrt></mfrac><mo>=</mo><mfrac><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><msqrt><mn>2</mn></msqrt></mfrac><mo>+</mo><mfrac><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><msqrt><mn>2</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow><msqrt><mn>2</mn></msqrt></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow><msqrt><mn>2</mn></msqrt></mfrac><mo>=</mo><msqrt><mn>6</mn></msqrt></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | Rút gọn các căn thức sau:
$ \text{\hspace{0.17em}}\sqrt{\frac{1}{2}}+\sqrt{4,5}+\sqrt{12,5}$ | $ \begin{array}{l}\sqrt{\frac{1}{2}}+\sqrt{4,5}+\sqrt{12,5}=\sqrt{\frac{1}{2}}+\sqrt{\frac{9}{2}}+\sqrt{\frac{25}{2}}\\ =\frac{\sqrt{2}+3\sqrt{2}+5\sqrt{2}}{2}=\frac{9\sqrt{2}}{2}\end{array}$ | https://khoahoc.vietjack.com/question/1008971 | ### Câu hỏi:
Rút gọn các căn thức sau:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msqrt><mfrac><mn>1</mn><mn>2</mn></mfrac></msqrt><mo>+</mo><msqrt><mn>4</mn><mo>,</mo><mn>5</mn></msqrt><mo>+</mo><msqrt><mn>12</mn><mo>,</mo><mn>5</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mfrac><mn>1</mn><mn>2</mn></mfrac></msqrt><mo>+</mo><msqrt><mn>4</mn><mo>,</mo><mn>5</mn></msqrt><mo>+</mo><msqrt><mn>12</mn><mo>,</mo><mn>5</mn></msqrt><mo>=</mo><msqrt><mfrac><mn>1</mn><mn>2</mn></mfrac></msqrt><mo>+</mo><msqrt><mfrac><mn>9</mn><mn>2</mn></mfrac></msqrt><mo>+</mo><msqrt><mfrac><mn>25</mn><mn>2</mn></mfrac></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>5</mn><msqrt><mn>2</mn></msqrt></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>9</mn><msqrt><mn>2</mn></msqrt></mrow><mn>2</mn></mfrac></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}$ | $\begin{aligned}
\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}} &= \frac{\sqrt{2}.\left(2+\sqrt{3}\right)}{2+\sqrt{4+2\sqrt{3}}}+\frac{\sqrt{2}.\left(2-\sqrt{3}\right)}{2-\sqrt{4-2\sqrt{3}}} \\
&= \frac{2\sqrt{2}+\sqrt{6}}{2+\sqrt{3}+1}+\frac{2\sqrt{2}-\sqrt{6}}{2-\sqrt{3}+1} = \frac{2\sqrt{2}+6}{3+\sqrt{3}}+\frac{2\sqrt{2}-\sqrt{6}}{3-\sqrt{3}} \\
&= \frac{\left(2\sqrt{2}+6\right)\left(3-\sqrt{3}\right)+\left(2\sqrt{2}-\sqrt{6}\right)\left(3+\sqrt{3}\right)}{3^2-\left(\sqrt{3}\right)^2} \\
&= \frac{6\sqrt{2}+3\sqrt{6}-2\sqrt{6}-3\sqrt{2}+6\sqrt{2}-3\sqrt{6}-2\sqrt{6}+3\sqrt{2}}{9-3} = \frac{12\sqrt{2}-4\sqrt{6}}{3} = 4\sqrt{2}-\frac{4}{3}\sqrt{6}
\end{aligned}$ | https://khoahoc.vietjack.com/question/1008977 | ### Câu hỏi:
$\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}$
### Lời giải:
$\begin{aligned}
\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}} &= \frac{\sqrt{2}.\left(2+\sqrt{3}\right)}{2+\sqrt{4+2\sqrt{3}}}+\frac{\sqrt{2}.\left(2-\sqrt{3}\right)}{2-\sqrt{4-2\sqrt{3}}} \\
&= \frac{2\sqrt{2}+\sqrt{6}}{2+\sqrt{3}+1}+\frac{2\sqrt{2}-\sqrt{6}}{2-\sqrt{3}+1} = \frac{2\sqrt{2}+6}{3+\sqrt{3}}+\frac{2\sqrt{2}-\sqrt{6}}{3-\sqrt{3}} \\
&= \frac{\left(2\sqrt{2}+6\right)\left(3-\sqrt{3}\right)+\left(2\sqrt{2}-\sqrt{6}\right)\left(3+\sqrt{3}\right)}{3^2-\left(\sqrt{3}\right)^2} \\
&= \frac{6\sqrt{2}+3\sqrt{6}-2\sqrt{6}-3\sqrt{2}+6\sqrt{2}-3\sqrt{6}-2\sqrt{6}+3\sqrt{2}}{9-3} = \frac{12\sqrt{2}-4\sqrt{6}}{3} = 4\sqrt{2}-\frac{4}{3}\sqrt{6}
\end{aligned}$
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Free Form | Lớp 9 | Rút gọn các căn thức sau:
$ \sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}$ | $ \begin{array}{l}\sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}\\ =\sqrt{{\left(\sqrt{3}-2\right)}^{2}}-\sqrt{{\left(\sqrt{3}+2\right)}^{2}}=\left|\sqrt{3}-2\right|-\left|\sqrt{3}+2\right|\\ =\sqrt{3}-2-\sqrt{3}-2=-4\end{array}$ | https://khoahoc.vietjack.com/question/1008984 | ### Câu hỏi:
Rút gọn các căn thức sau:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>7</mn><mo>−</mo><mn>4</mn><msqrt><mn>3</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>7</mn><mo>+</mo><mn>4</mn><msqrt><mn>3</mn></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>7</mn><mo>−</mo><mn>4</mn><msqrt><mn>3</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>7</mn><mo>+</mo><mn>4</mn><msqrt><mn>3</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><mfenced close="|" open="|"><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mo>−</mo><mfenced close="|" open="|"><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><mo>=</mo><mo>−</mo><mn>4</mn></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $ \begin{array}{l}\text{\hspace{0.17em}}\left(\frac{\sqrt{38}-\sqrt{19}}{1-\sqrt{2}}+\frac{\sqrt{45}-\sqrt{15}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{19}-\sqrt{15}}\end{array}$ | $ \begin{array}{l}\left(\frac{\sqrt{38}-\sqrt{19}}{1-\sqrt{2}}+\frac{\sqrt{45}-\sqrt{15}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{19}-\sqrt{15}}\\ =\left[\frac{-\sqrt{19}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}-\frac{\sqrt{15}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}\right].\frac{\sqrt{19}-\sqrt{15}}{1}\\ =\left(-\sqrt{19}-\sqrt{15}\right).\left(\sqrt{19}-\sqrt{15}\right)\\ =-\left(\sqrt{19}+\sqrt{15}\right).\left(\sqrt{19}-\sqrt{15}\right)=-4\text{\hspace{0.17em}}\end{array}$ | https://khoahoc.vietjack.com/question/1008988 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mfenced><mrow><mfrac><mrow><msqrt><mn>38</mn></msqrt><mo>−</mo><msqrt><mn>19</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>45</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mrow></mfenced><mo>:</mo><mfrac><mn>1</mn><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfrac></mtd></mtr></mtable></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mfrac><mrow><msqrt><mn>38</mn></msqrt><mo>−</mo><msqrt><mn>19</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>45</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mrow></mfenced><mo>:</mo><mfrac><mn>1</mn><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mo>−</mo><msqrt><mn>19</mn></msqrt><mfenced><mrow><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>−</mo><mfrac><mrow><msqrt><mn>15</mn></msqrt><mfenced><mrow><mn>1</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mrow></mfenced><mo>.</mo><mfrac><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow><mn>1</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mo>−</mo><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mo>.</mo><mfenced><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mo>−</mo><mfenced><mrow><msqrt><mn>19</mn></msqrt><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mo>.</mo><mfenced><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mo>=</mo><mo>−</mo><mn>4</mn><mtext> </mtext></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $ D=\left(\frac{2\sqrt{x}+x}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\left(1-\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\left(\begin{array}{l}x>0\\ x\ne 1\end{array}\right)$ | $ \begin{array}{l}D=\left(\frac{2\sqrt{x}+2}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\left(1-\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\left(\begin{array}{l}x>0\\ x\ne 1\end{array}\right)\\ =\frac{2\sqrt{x}+x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\frac{x+\sqrt{x}+1}{x-1}\\ =\frac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x-1\right)}=\frac{1}{x-1}\end{array}$ | https://khoahoc.vietjack.com/question/1008991 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced><mrow><mfrac><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mi>x</mi></mrow><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>:</mo><mfenced><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mfenced><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>≠</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>D</mi><mo>=</mo><mfenced><mrow><mfrac><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>:</mo><mfenced><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mfenced><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>≠</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mi>x</mi><mo>−</mo><mi>x</mi><mo>−</mo><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow><mrow><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>.</mo><mfrac><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow><mrow><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | Rút gọn
$ A=\sqrt{\frac{m}{1-2x+{x}^{2}}}+\sqrt{\frac{4m-8mx+4m{x}^{2}}{81}}\left(\begin{array}{l}x>1\\ m\ge 0\end{array}\right)$ | $ \begin{array}{l}A=\sqrt{\frac{m}{1-2x+{x}^{2}}}+\sqrt{\frac{4m-8mx+4m{x}^{2}}{81}}\left(\begin{array}{l}x>0\\ m\ge 0\end{array}\right)\\ =\frac{\sqrt{m}}{\sqrt{{\left(x-1\right)}^{2}}}+\frac{\sqrt{4m}.\sqrt{{x}^{2}-2x+1}}{\sqrt{81}}=\frac{\sqrt{m}}{x-1}+\frac{2\sqrt{m}.(x-1)}{9}\\ =\frac{9\sqrt{m}+2\sqrt{m}{\left(x-1\right)}^{2}}{9\left(x-1\right)}\end{array}$ | https://khoahoc.vietjack.com/question/1008994 | ### Câu hỏi:
Rút gọn
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msqrt><mfrac><mi>m</mi><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></msqrt><mo>+</mo><msqrt><mfrac><mrow><mn>4</mn><mi>m</mi><mo>−</mo><mn>8</mn><mi>m</mi><mi>x</mi><mo>+</mo><mn>4</mn><mi>m</mi><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>81</mn></mfrac></msqrt><mfenced><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>></mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>m</mi><mo>≥</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>A</mi><mo>=</mo><msqrt><mfrac><mi>m</mi><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></msqrt><mo>+</mo><msqrt><mfrac><mrow><mn>4</mn><mi>m</mi><mo>−</mo><mn>8</mn><mi>m</mi><mi>x</mi><mo>+</mo><mn>4</mn><mi>m</mi><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>81</mn></mfrac></msqrt><mfenced><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>m</mi><mo>≥</mo><mn>0</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><msqrt><mi>m</mi></msqrt><msqrt><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>4</mn><mi>m</mi></msqrt><mo>.</mo><msqrt><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></msqrt></mrow><msqrt><mn>81</mn></msqrt></mfrac><mo>=</mo><mfrac><msqrt><mi>m</mi></msqrt><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>m</mi></msqrt><mo>.</mo><mo>(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mn>9</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>9</mn><msqrt><mi>m</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>m</mi></msqrt><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mn>9</mn><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | Rút gọn
$ B=\sqrt{64a{b}^{3}}-3\sqrt{121{a}^{3}{b}^{3}}+2ab\sqrt{9ab}-5b\sqrt{81{a}^{3}b}\left(a,b>0\right)$ | $ \begin{array}{l}B=\sqrt{64a{b}^{3}}-3\sqrt{121{a}^{3}{b}^{3}}+2ab\sqrt{9ab}-5b\sqrt{81{a}^{3}b}\\ =8b\sqrt{ab}-3.11ab\sqrt{ab}+2.3ab\sqrt{ab}-5b.9a\sqrt{ab}\\ =8b\sqrt{ab}-33ab\sqrt{ab}+6ab\sqrt{ab}-45ab\sqrt{ab}\\ =8b\sqrt{ab}-72ab\sqrt{ab}\end{array}$ | https://khoahoc.vietjack.com/question/1008996 | ### Câu hỏi:
Rút gọn
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><msqrt><mn>64</mn><mi>a</mi><msup><mi>b</mi><mn>3</mn></msup></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>121</mn><msup><mi>a</mi><mn>3</mn></msup><msup><mi>b</mi><mn>3</mn></msup></msqrt><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><msqrt><mn>9</mn><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>5</mn><mi>b</mi><msqrt><mn>81</mn><msup><mi>a</mi><mn>3</mn></msup><mi>b</mi></msqrt><mfenced><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></mrow></mfenced></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>B</mi><mo>=</mo><msqrt><mn>64</mn><mi>a</mi><msup><mi>b</mi><mn>3</mn></msup></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>121</mn><msup><mi>a</mi><mn>3</mn></msup><msup><mi>b</mi><mn>3</mn></msup></msqrt><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><msqrt><mn>9</mn><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>5</mn><mi>b</mi><msqrt><mn>81</mn><msup><mi>a</mi><mn>3</mn></msup><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>8</mn><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>3.11</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mn>2.3</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>5</mn><mi>b</mi><mn>.9</mn><mi>a</mi><msqrt><mi>a</mi><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>8</mn><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>33</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mn>6</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>45</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>8</mn><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>72</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ S=\left(\frac{\sqrt{a}+a}{1+\sqrt{a}}\right).\left(\frac{a-3\sqrt{a}+2}{\sqrt{a}-2}\right)\left(\begin{array}{l}a>0\\ a\ne 4\end{array}\right)$ | $ \begin{array}{l}S=\left(\frac{\sqrt{a}+a}{1+\sqrt{a}}\right).\left(\frac{a-3\sqrt{a}+2}{\sqrt{a}-2}\right)\left(\begin{array}{l}a>0\\ a\ne 4\end{array}\right)\\ =\frac{\sqrt{a}.\left(1+\sqrt{a}\right)}{1+\sqrt{a}}.\frac{a-\sqrt{a}-2\sqrt{a}+2}{\sqrt{a}-2}\\ =\sqrt{a}.\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}{\sqrt{a}-2}=\sqrt{a}.\left(\sqrt{a}-1\right)=a-\sqrt{a}\end{array}$ | https://khoahoc.vietjack.com/question/1008999 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfenced><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mi>a</mi></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfrac></mfenced><mo>.</mo><mfenced><mfrac><mrow><mi>a</mi><mo>−</mo><mn>3</mn><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac></mfenced><mfenced><mtable columnalign="left"><mtr><mtd><mi>a</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>≠</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>S</mi><mo>=</mo><mfenced><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mi>a</mi></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfrac></mfenced><mo>.</mo><mfenced><mfrac><mrow><mi>a</mi><mo>−</mo><mn>3</mn><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac></mfenced><mfenced><mtable columnalign="left"><mtr><mtd><mi>a</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>≠</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>.</mo><mfenced><mrow><mn>1</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfenced></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfrac><mo>.</mo><mfrac><mrow><mi>a</mi><mo>−</mo><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>.</mo><mfrac><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>.</mo><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mi>a</mi><mo>−</mo><msqrt><mi>a</mi></msqrt></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $\sqrt{4x^2-4x+1}-\sqrt{9x^2}=0$ | $\begin{aligned}
\sqrt{4x^2-4x+1}-\sqrt{9x^2}&=0\\
\Leftrightarrow \sqrt{(2x-1)^2}-\sqrt{(3x)^2}&=0\\
\Leftrightarrow |2x-1|&=|3x|\\
\Leftrightarrow \left[
\begin{aligned}
2x-1&=3x\\
2x-1&=-3x
\end{aligned}
\right.
\Rightarrow \left[
\begin{aligned}
x&=-1\\
x&=\frac{1}{5}
\end{aligned}
\right.
\end{aligned}$ | https://khoahoc.vietjack.com/question/1009002 | ### Câu hỏi:
$\sqrt{4x^2-4x+1}-\sqrt{9x^2}=0$
### Lời giải:
$\begin{aligned}
\sqrt{4x^2-4x+1}-\sqrt{9x^2}&=0\\
\Leftrightarrow \sqrt{(2x-1)^2}-\sqrt{(3x)^2}&=0\\
\Leftrightarrow |2x-1|&=|3x|\\
\Leftrightarrow \left[
\begin{aligned}
2x-1&=3x\\
2x-1&=-3x
\end{aligned}
\right.
\Rightarrow \left[
\begin{aligned}
x&=-1\\
x&=\frac{1}{5}
\end{aligned}
\right.
\end{aligned}$
|
Free Form | Lớp 9 | $\sqrt{3x-5}+\sqrt{2x-3}=\sqrt{x+2}$ | $\begin{aligned}
\sqrt{3x-5}+\sqrt{2x-3}&=\sqrt{x+2} \left(x\geq \frac{5}{3}\right)\\
\Leftrightarrow \sqrt{3x-5}&=\sqrt{x+2}-\sqrt{2x-3}\\
\Rightarrow 3x-5&=x+2+2x-3-2\sqrt{(x+2)(2x-3)}\\
\Leftrightarrow \sqrt{(x+2)(2x-3)}&=2 \Leftrightarrow 2x^2+x-6=4\\
\Leftrightarrow 2x^2+x-10&=0 \Leftrightarrow \left[
\begin{aligned}
x&=2 (tm)\\
x&=-\frac{5}{2} (ktm)
\end{aligned}
\right.
\end{aligned}$ | https://khoahoc.vietjack.com/question/1009005 | ### Câu hỏi:
$\sqrt{3x-5}+\sqrt{2x-3}=\sqrt{x+2}$
### Lời giải:
$\begin{aligned}
\sqrt{3x-5}+\sqrt{2x-3}&=\sqrt{x+2} \left(x\geq \frac{5}{3}\right)\\
\Leftrightarrow \sqrt{3x-5}&=\sqrt{x+2}-\sqrt{2x-3}\\
\Rightarrow 3x-5&=x+2+2x-3-2\sqrt{(x+2)(2x-3)}\\
\Leftrightarrow \sqrt{(x+2)(2x-3)}&=2 \Leftrightarrow 2x^2+x-6=4\\
\Leftrightarrow 2x^2+x-10&=0 \Leftrightarrow \left[
\begin{aligned}
x&=2 (tm)\\
x&=-\frac{5}{2} (ktm)
\end{aligned}
\right.
\end{aligned}$
|
Free Form | Lớp 9 | $ \frac{2{x}^{2}}{3-\sqrt{{\left(9+2x\right)}^{2}}}=x+9$ | $ \frac{2{x}^{2}}{3-\sqrt{{\left(9+2x\right)}^{2}}}=x+9\Leftrightarrow \frac{2{x}^{2}}{3-\left|9+2x\right|}=x+9$
$ \begin{array}{l}x\ge \frac{-9}{2}\Rightarrow \frac{2{x}^{2}}{3-9-2x}=x+9\\ \Leftrightarrow 2{x}^{2}+24x=-54+2{x}^{2}\\ \Rightarrow x=-\frac{9}{4}\left(tm\right)\\ x<-\frac{9}{2}\Rightarrow \frac{2{x}^{2}}{3+9+2x}=x+9\\ \Leftrightarrow 2{x}^{2}=2{x}^{2}+30x+108\\ \Rightarrow x=-\frac{-18}{5}\left(ktm\right)\text{\hspace{0.17em}\hspace{0.17em}}Vay\text{\hspace{0.17em}}x=\frac{-9}{4}\end{array}$ | https://khoahoc.vietjack.com/question/1009010 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>9</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced><mn>2</mn></msup></msqrt></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>9</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced><mn>2</mn></msup></msqrt></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn><mo>⇔</mo><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>−</mo><mfenced close="|" open="|"><mrow><mn>9</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>≥</mo><mfrac><mrow><mo>−</mo><mn>9</mn></mrow><mn>2</mn></mfrac><mo>⇒</mo><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>−</mo><mn>9</mn><mo>−</mo><mn>2</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mi>x</mi><mo>=</mo><mo>−</mo><mn>54</mn><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>=</mo><mo>−</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>x</mi><mo><</mo><mo>−</mo><mfrac><mn>9</mn><mn>2</mn></mfrac><mo>⇒</mo><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>30</mn><mi>x</mi><mo>+</mo><mn>108</mn></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>=</mo><mo>−</mo><mfrac><mrow><mo>−</mo><mn>18</mn></mrow><mn>5</mn></mfrac><mo>(</mo><mi>k</mi><mi>t</mi><mi>m</mi><mo>)</mo><mtext> </mtext><mi>V</mi><mi>a</mi><mi>y</mi><mtext> </mtext><mi>x</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>9</mn></mrow><mn>4</mn></mfrac></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | Giải phương trình:
$ 4\sqrt{2x}-2\sqrt{18x}+\sqrt{32x}=3$ | $ \begin{array}{l}4\sqrt{2x}-2\sqrt{18x}+\sqrt{32x}=3\\ \Leftrightarrow 4\sqrt{2x}-2.3\sqrt{2x}+4\sqrt{2x}=3\left(x\ge 0\right)\\ \Leftrightarrow 2\sqrt{2x}=3\Rightarrow 2x=\frac{9}{4}\Rightarrow x=\frac{9}{8}\left(tm\right)\end{array}$ | https://khoahoc.vietjack.com/question/1009011 | ### Câu hỏi:
Giải phương trình:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>18</mn><mi>x</mi></msqrt><mo>+</mo><msqrt><mn>32</mn><mi>x</mi></msqrt><mo>=</mo><mn>3</mn></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mn>4</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>18</mn><mi>x</mi></msqrt><mo>+</mo><msqrt><mn>32</mn><mi>x</mi></msqrt><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>4</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>−</mo><mn>2.3</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>+</mo><mn>4</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>=</mo><mn>3</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mn>0</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>=</mo><mn>3</mn><mo>⇒</mo><mn>2</mn><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>8</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ \sqrt{x+4}+\sqrt{x-1}=2$ | $ \begin{array}{l}\\ x+4+x-1+2\sqrt{\left(x+4\right)\left(x-1\right)}=2\\ \Leftrightarrow 4\left(x+4\right)\left(x-1\right)={\left(-2x-1\right)}^{2}\\ \Leftrightarrow 4{x}^{2}+12x-16=4{x}^{2}+4x+1\\ \Leftrightarrow x=\frac{17}{8}\left(tm\right)\end{array}$ | https://khoahoc.vietjack.com/question/1009017 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>x</mi><mo>+</mo><mn>4</mn></msqrt><mo>+</mo><msqrt><mi>x</mi><mo>−</mo><mn>1</mn></msqrt><mo>=</mo><mn>2</mn></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mn>4</mn><mo>+</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>+</mo><mn>2</mn><msqrt><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced></msqrt><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>4</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mo>=</mo><msup><mfenced><mrow><mo>−</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mi>x</mi><mo>−</mo><mn>16</mn><mo>=</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mi>x</mi><mo>=</mo><mfrac><mn>17</mn><mn>8</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $\sqrt{44}-\sqrt{176}+2\sqrt{275}$ | $\sqrt{44}-\sqrt{176}+2\sqrt{275}=2\sqrt{11}-4\sqrt{11}+10\sqrt{11}=8\sqrt{11}$ | https://khoahoc.vietjack.com/question/1009018 | ### Câu hỏi:
$\sqrt{44}-\sqrt{176}+2\sqrt{275}$
### Lời giải:
$\sqrt{44}-\sqrt{176}+2\sqrt{275}=2\sqrt{11}-4\sqrt{11}+10\sqrt{11}=8\sqrt{11}$
|
Free Form | Lớp 9 | <p>Tính</p>
<p>$ 5\sqrt{3}-3\sqrt{48}+2\sqrt{75}-\frac{1}{3}\sqrt{108}$</p> | <p>$ 5\sqrt{3}-3\sqrt{48}+2\sqrt{75}-\frac{1}{3}\sqrt{108}=5\sqrt{3}-12\sqrt{3}+10\sqrt{3}-2\sqrt{3}=\sqrt{3}$</p> | https://khoahoc.vietjack.com/question/1009020 | ### Câu hỏi:
<p>Tính</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>48</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>75</mn></msqrt><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>108</mn></msqrt></math></p>
### Lời giải:
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>48</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>75</mn></msqrt><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>108</mn></msqrt><mo>=</mo><mn>5</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>12</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>10</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>=</mo><msqrt><mn>3</mn></msqrt></math></p>
|
Free Form | Lớp 9 | <p>Tính</p>
<p>$ \sqrt{343}-\sqrt{112}-\sqrt{63}-\sqrt{21}$</p> | <p>$ \sqrt{343}-\sqrt{112}-\sqrt{63}-\sqrt{21}=7\sqrt{7}-4\sqrt{7}-3\sqrt{7}-\sqrt{21}=-\sqrt{21}$</p> | https://khoahoc.vietjack.com/question/1009023 | ### Câu hỏi:
<p>Tính</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>343</mn></msqrt><mo>−</mo><msqrt><mn>112</mn></msqrt><mo>−</mo><msqrt><mn>63</mn></msqrt><mo>−</mo><msqrt><mn>21</mn></msqrt></math></p>
### Lời giải:
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>343</mn></msqrt><mo>−</mo><msqrt><mn>112</mn></msqrt><mo>−</mo><msqrt><mn>63</mn></msqrt><mo>−</mo><msqrt><mn>21</mn></msqrt><mo>=</mo><mn>7</mn><msqrt><mn>7</mn></msqrt><mo>−</mo><mn>4</mn><msqrt><mn>7</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>21</mn></msqrt><mo>=</mo><mo>−</mo><msqrt><mn>21</mn></msqrt></math></p>
|
Free Form | Lớp 9 | <p>Tính</p>
$ \sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}$ | $ \begin{array}{l}\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}=\sqrt{6+2\sqrt{2}.\sqrt{3-\left(\sqrt{3}+1\right)}}\\ =\sqrt{6+2\sqrt{2}.\sqrt{2-\sqrt{3}}}=\sqrt{6+2\sqrt{4-2\sqrt{3}}}\\ =\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{6+2\sqrt{3}-2}\\ =\sqrt{4+2\sqrt{3}}=\sqrt{{\left(\sqrt{3}+1\right)}^{2}}=\sqrt{3}+1\end{array}$ | https://khoahoc.vietjack.com/question/1009024 | ### Câu hỏi:
<p>Tính</p>
<math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></msqrt></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>4</mn><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | <p>Tính</p>
<p>$ \sqrt{28+\sqrt{300}}+\sqrt{19-\sqrt{192}}$</p> | <p>$ \begin{array}{l}\sqrt{28+\sqrt{300}}+\sqrt{19-\sqrt{192}}\\ =\sqrt{28+10\sqrt{3}}+\sqrt{19-8\sqrt{3}}\\ =\sqrt{{5}^{2}+\mathrm{2.5.}\sqrt{3}+{\left(\sqrt{3}\right)}^{2}}+\sqrt{{4}^{2}-\mathrm{2.4.}\sqrt{3}+{\left(\sqrt{3}\right)}^{2}}\\ =\sqrt{{\left(5+\sqrt{3}\right)}^{2}}+\sqrt{{\left(4-\sqrt{3}\right)}^{2}}\\ =5+\sqrt{3}+4-\sqrt{3}=9\end{array}$</p> | https://khoahoc.vietjack.com/question/1009028 | ### Câu hỏi:
<p>Tính</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>28</mn><mo>+</mo><msqrt><mn>300</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>19</mn><mo>−</mo><msqrt><mn>192</mn></msqrt></msqrt></math></p>
### Lời giải:
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>28</mn><mo>+</mo><msqrt><mn>300</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>19</mn><mo>−</mo><msqrt><mn>192</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>28</mn><mo>+</mo><mn>10</mn><msqrt><mn>3</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>19</mn><mo>−</mo><mn>8</mn><msqrt><mn>3</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mn>2.5.</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><msup><mfenced><msqrt><mn>3</mn></msqrt></mfenced><mn>2</mn></msup></msqrt><mo>+</mo><msqrt><msup><mn>4</mn><mn>2</mn></msup><mo>−</mo><mn>2.4.</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><msup><mfenced><msqrt><mn>3</mn></msqrt></mfenced><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mfenced><mrow><mn>5</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt><mo>+</mo><msqrt><msup><mfenced><mrow><mn>4</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>5</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>4</mn><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>=</mo><mn>9</mn></mtd></mtr></mtable></math></p>
|
Free Form | Lớp 9 | <p>Tính</p>
<div>$ \begin{array}{l}\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\end{array}$</div> | <div>$ \begin{array}{l}\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}=\frac{{\left(\sqrt{7}+\sqrt{5}\right)}^{2}+{\left(\sqrt{7}-\sqrt{5}\right)}^{2}}{\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}\\ =\frac{12+2\sqrt{35}+12-2\sqrt{35}}{7-5}=\frac{24}{2}=12\end{array}$</div> | https://khoahoc.vietjack.com/question/1009034 | ### Câu hỏi:
<p>Tính</p>
<div><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac></mtd></mtr></mtable></math></div>
### Lời giải:
<div><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mfenced><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mfenced><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>12</mn><mo>+</mo><mn>2</mn><msqrt><mn>35</mn></msqrt><mo>+</mo><mn>12</mn><mo>−</mo><mn>2</mn><msqrt><mn>35</mn></msqrt></mrow><mrow><mn>7</mn><mo>−</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mfrac><mn>24</mn><mn>2</mn></mfrac><mo>=</mo><mn>12</mn></mtd></mtr></mtable></math></div>
|
Free Form | Lớp 9 | Phân tích đa thức thành nhân tử
$ a+\sqrt{a}+2\sqrt{ab}+2\sqrt{b}$ | $ \begin{array}{l}a+\sqrt{a}+2\sqrt{ab}+2\sqrt{b}\\ =\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)\\ =\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\end{array}$ | https://khoahoc.vietjack.com/question/1009046 | ### Câu hỏi:
Phân tích đa thức thành nhân tử
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>b</mi></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>a</mi><mo>+</mo><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mi>a</mi></msqrt><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>2</mn><msqrt><mi>b</mi></msqrt><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow></mfenced></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ {\left(1+\sqrt{x}\right)}^{2}-4\sqrt{x}$ | $ \begin{array}{l}{\left(1+\sqrt{x}\right)}^{2}-4\sqrt{x}\\ =1+2\sqrt{x}+x-4\sqrt{x}\\ =x-2\sqrt{x}+1\\ ={\left(\sqrt{x}-1\right)}^{2}\end{array}$ | https://khoahoc.vietjack.com/question/1009050 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>+</mo><msqrt><mi>x</mi></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>4</mn><msqrt><mi>x</mi></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msup><mfenced><mrow><mn>1</mn><mo>+</mo><msqrt><mi>x</mi></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>4</mn><msqrt><mi>x</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>1</mn><mo>+</mo><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mi>x</mi><mo>−</mo><mn>4</mn><msqrt><mi>x</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mi>x</mi><mo>−</mo><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>=</mo><msup><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ b\sqrt{b}-4b+4\sqrt{b}-a\sqrt{b}$ | $ \begin{array}{l}\text{\hspace{0.17em}}b\sqrt{b}-4b+4\sqrt{b}-a\sqrt{b}\\ =\sqrt{b}\left[\left(b-4\sqrt{b}+4\right)-a\right]=\sqrt{b}\left[{\left(\sqrt{b}-2\right)}^{2}-{\left(\sqrt{a}\right)}^{2}\right]\\ =\sqrt{b}\left(\sqrt{b}-2-\sqrt{a}\right)\left(\sqrt{b}-2+\sqrt{a}\right)\end{array}$ | https://khoahoc.vietjack.com/question/1009055 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>4</mn><mi>b</mi><mo>+</mo><mn>4</mn><msqrt><mi>b</mi></msqrt><mo>−</mo><mi>a</mi><msqrt><mi>b</mi></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mi>b</mi><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>4</mn><mi>b</mi><mo>+</mo><mn>4</mn><msqrt><mi>b</mi></msqrt><mo>−</mo><mi>a</mi><msqrt><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mi>b</mi></msqrt><mfenced close="]" open="["><mrow><mfenced><mrow><mi>b</mi><mo>−</mo><mn>4</mn><msqrt><mi>b</mi></msqrt><mo>+</mo><mn>4</mn></mrow></mfenced><mo>−</mo><mi>a</mi></mrow></mfenced><mo>=</mo><msqrt><mi>b</mi></msqrt><mfenced close="]" open="["><mrow><msup><mfenced><mrow><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>−</mo><msup><mfenced><msqrt><mi>a</mi></msqrt></mfenced><mn>2</mn></msup></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mi>b</mi></msqrt><mfenced><mrow><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>2</mn><mo>−</mo><msqrt><mi>a</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>2</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfenced></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | Tìm x:
$ \sqrt[3]{x-5}=0,9$ | $ \sqrt[3]{x-5}=0,9\Leftrightarrow x-5=0,{9}^{3}\Leftrightarrow x=5,729$. Vậy x = 5,729. | https://khoahoc.vietjack.com/question/1009069 | ### Câu hỏi:
Tìm x:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>−</mo><mn>5</mn></mrow><mn>3</mn></mroot><mo>=</mo><mn>0</mn><mo>,</mo><mn>9</mn></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>−</mo><mn>5</mn></mrow><mn>3</mn></mroot><mo>=</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>⇔</mo><mi>x</mi><mo>−</mo><mn>5</mn><mo>=</mo><mn>0</mn><mo>,</mo><msup><mn>9</mn><mn>3</mn></msup><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>5</mn><mo>,</mo><mn>729</mn></math>. Vậy x = 5,729.
|
Free Form | Lớp 9 | Rút gọn biểu thức :
$ B=\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}$ | $ \begin{array}{l}B=\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}\\ \Rightarrow B\sqrt{2}=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\\ =\sqrt{{\left(\sqrt{5}+1\right)}^{2}}-\sqrt{{\left(\sqrt{5}-1\right)}^{2}}=\sqrt{5}+1-\left|\sqrt{5}-1\right|\\ =\sqrt{5}+1-\sqrt{5}+1=2\Rightarrow B=\sqrt{2}\left(do\text{\hspace{0.17em}}B>0\right)\end{array}$ | https://khoahoc.vietjack.com/question/1009079 | ### Câu hỏi:
Rút gọn biểu thức :
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><msqrt><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>B</mi><mo>=</mo><msqrt><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>B</mi><msqrt><mn>2</mn></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><mfenced close="|" open="|"><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn><mo>=</mo><mn>2</mn><mo>⇒</mo><mi>B</mi><mo>=</mo><msqrt><mn>2</mn></msqrt><mfenced><mrow><mi>d</mi><mi>o</mi><mtext> </mtext><mi>B</mi><mo>></mo><mn>0</mn></mrow></mfenced></mtd></mtr></mtable></math>
|
Free Form | Lớp 9 | $ C=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$ | $ \begin{array}{l}\text{\hspace{0.17em}}C=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}\right)}^{2}-2.2\sqrt{5}.3+{3}^{2}}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}-3\right)}^{2}}}}\\ =\sqrt{\sqrt{5-\sqrt{3-\left(2\sqrt{5}-3\right)}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-2\sqrt{5}+3}}\\ =\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\\ =\sqrt{\sqrt{5}-\sqrt{{\left(\sqrt{5}-1\right)}^{2}}}=\sqrt{\sqrt{5}-\left|\sqrt{5}-1\right|}=\sqrt{\sqrt{5}-\sqrt{5}+1}=\sqrt{1}=1\end{array}$ | https://khoahoc.vietjack.com/question/1009082 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mi>C</mi><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.2</mn><msqrt><mn>5</mn></msqrt><mn>.3</mn><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><mfenced close="|" open="|"><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $D = \sqrt{3 - \sqrt{5}} (\sqrt{10} - \sqrt{2}) (3 + \sqrt{5})$ | $\begin{aligned}
D &= \sqrt{3 - \sqrt{5}} (\sqrt{10} - \sqrt{2}) (3 + \sqrt{5}) \\
&= \sqrt{2(3 - \sqrt{5})} . (\sqrt{5} - 1) (3 + \sqrt{5}) \\
&= \sqrt{6 - 2\sqrt{5}} . (\sqrt{5} - 1) (3 + \sqrt{5}) \\
&= (\sqrt{5} - 1) (\sqrt{5} - 1) (3 + \sqrt{5}) \\
&= (\sqrt{5} - 1)^2 . (3 + \sqrt{5}) = (6 - 2\sqrt{5}) (3 + \sqrt{5}) \\
&= 18 - 6\sqrt{5} + 6\sqrt{5} - 10 = 8
\end{aligned}$ | https://khoahoc.vietjack.com/question/1009085 | ### Câu hỏi:
$D = \sqrt{3 - \sqrt{5}} (\sqrt{10} - \sqrt{2}) (3 + \sqrt{5})$
### Lời giải:
$\begin{aligned}
D &= \sqrt{3 - \sqrt{5}} (\sqrt{10} - \sqrt{2}) (3 + \sqrt{5}) \\
&= \sqrt{2(3 - \sqrt{5})} . (\sqrt{5} - 1) (3 + \sqrt{5}) \\
&= \sqrt{6 - 2\sqrt{5}} . (\sqrt{5} - 1) (3 + \sqrt{5}) \\
&= (\sqrt{5} - 1) (\sqrt{5} - 1) (3 + \sqrt{5}) \\
&= (\sqrt{5} - 1)^2 . (3 + \sqrt{5}) = (6 - 2\sqrt{5}) (3 + \sqrt{5}) \\
&= 18 - 6\sqrt{5} + 6\sqrt{5} - 10 = 8
\end{aligned}$
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Free Form | Lớp 9 | $ G=\frac{1+\frac{\sqrt{3}}{2}}{1+\sqrt{1+\frac{\sqrt{3}}{2}}}+\frac{1-\frac{\sqrt{3}}{2}}{1-\sqrt{1-\frac{\sqrt{3}}{2}}}$ | $ \begin{array}{l}\text{\hspace{0.17em}}G=\frac{1+\frac{\sqrt{3}}{2}}{1+\sqrt{1+\frac{\sqrt{3}}{2}}}+\frac{1-\frac{\sqrt{3}}{2}}{1-\sqrt{1-\frac{\sqrt{3}}{2}}}=\frac{\frac{2+\sqrt{3}}{2}}{\frac{\sqrt{2}+\sqrt{2+\sqrt{3}}}{\sqrt{2}}}+\frac{\frac{2-\sqrt{3}}{2}}{\frac{\sqrt{2}-\sqrt{2-\sqrt{3}}}{\sqrt{2}}}\\ =\frac{2+\sqrt{3}}{2}.\frac{\sqrt{2}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{2}.\frac{\sqrt{2}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\end{array}$
$ \begin{array}{l}=\frac{2+\sqrt{3}}{\sqrt{2}.\left(\sqrt{2}+\sqrt{2+\sqrt{3}}\right)}+\frac{2-\sqrt{3}}{\sqrt{2}.\left(\sqrt{2}-\sqrt{2-\sqrt{3}}\right)}\\ =\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}=\frac{2+\sqrt{3}}{2+\sqrt{3}+1}+\frac{2-\sqrt{3}}{2-\left(\sqrt{3}-1\right)}\\ =\frac{2+\sqrt{3}}{3+\sqrt{3}}+\frac{2-\sqrt{3}}{3-\sqrt{3}}=\frac{\left(2+\sqrt{3}\right)\left(3-\sqrt{3}\right)+\left(2-\sqrt{3}\right)\left(3+\sqrt{3}\right)}{9-3}\\ =\frac{6-3+\sqrt{3}+6-3-\sqrt{3}}{6}=\frac{6}{6}=1\end{array}$ | https://khoahoc.vietjack.com/question/1009088 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>1</mn><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></msqrt></mrow></mfrac></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mi>G</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>1</mn><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></msqrt></mrow></mfrac><mo>=</mo><mfrac><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow><msqrt><mn>2</mn></msqrt></mfrac></mfrac><mo>+</mo><mfrac><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow><msqrt><mn>2</mn></msqrt></mfrac></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mo>.</mo><mfrac><msqrt><mn>2</mn></msqrt><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mo>.</mo><mfrac><msqrt><mn>2</mn></msqrt><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfrac></mtd></mtr></mtable></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>+</mo><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>−</mo><msqrt><mn>4</mn><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>−</mo><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><mn>9</mn><mo>−</mo><mn>3</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>6</mn><mo>−</mo><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>6</mn><mo>−</mo><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mn>6</mn></mfrac><mo>=</mo><mfrac><mn>6</mn><mn>6</mn></mfrac><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | Rút gọn biểu thức :
$ 2\sqrt{27}-\sqrt{\frac{16}{3}}-\sqrt{48}-\sqrt{8\frac{1}{3}}$ | $ \begin{array}{l}2\sqrt{27}-\sqrt{\frac{16}{3}}-\sqrt{48}-\sqrt{8\frac{1}{3}}\\ =2\sqrt{9.3}-\frac{\sqrt{16}}{\sqrt{3}}-\sqrt{16.3}-\frac{\sqrt{25}}{\sqrt{3}}\\ =2.3\sqrt{3}-\frac{4}{\sqrt{3}}-4\sqrt{3}-\frac{5}{\sqrt{3}}\\ =6\sqrt{3}-\frac{4}{3}\sqrt{3}-4\sqrt{3}-\frac{5}{3}\sqrt{3}=-\sqrt{3}\end{array}$ | https://khoahoc.vietjack.com/question/1009093 | ### Câu hỏi:
Rút gọn biểu thức :
<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mn>27</mn></msqrt><mo>−</mo><msqrt><mfrac><mn>16</mn><mn>3</mn></mfrac></msqrt><mo>−</mo><msqrt><mn>48</mn></msqrt><mo>−</mo><msqrt><mn>8</mn><mfrac><mn>1</mn><mn>3</mn></mfrac></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mn>2</mn><msqrt><mn>27</mn></msqrt><mo>−</mo><msqrt><mfrac><mn>16</mn><mn>3</mn></mfrac></msqrt><mo>−</mo><msqrt><mn>48</mn></msqrt><mo>−</mo><msqrt><mn>8</mn><mfrac><mn>1</mn><mn>3</mn></mfrac></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>2</mn><msqrt><mn>9.3</mn></msqrt><mo>−</mo><mfrac><msqrt><mn>16</mn></msqrt><msqrt><mn>3</mn></msqrt></mfrac><mo>−</mo><msqrt><mn>16.3</mn></msqrt><mo>−</mo><mfrac><msqrt><mn>25</mn></msqrt><msqrt><mn>3</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mn>2.3</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mfrac><mn>4</mn><msqrt><mn>3</mn></msqrt></mfrac><mo>−</mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mfrac><mn>5</mn><msqrt><mn>3</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mn>6</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><msqrt><mn>3</mn></msqrt><mo>=</mo><mo>−</mo><msqrt><mn>3</mn></msqrt></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $ \left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)$ | $ \begin{array}{l}\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\\ =\left(5\sqrt{5}-2\sqrt{3}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+3\sqrt{3}\right)\\ =\left(3\sqrt{5}-2\sqrt{3}\right)\left(3\sqrt{5}+2\sqrt{3}\right)\\ ={\left(3\sqrt{5}\right)}^{2}-{\left(2\sqrt{3}\right)}^{2}=45-12=33\end{array}$ | https://khoahoc.vietjack.com/question/1009096 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msqrt><mn>125</mn></msqrt><mo>−</mo><msqrt><mn>12</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>27</mn></msqrt></mrow></mfenced></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><msqrt><mn>125</mn></msqrt><mo>−</mo><msqrt><mn>12</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>27</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>5</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><msup><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><msup><mfenced><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>45</mn><mo>−</mo><mn>12</mn><mo>=</mo><mn>33</mn></mtd></mtr></mtable></math>
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Free Form | Lớp 9 | $ \left(3\sqrt{20}-\sqrt{125}-15\sqrt{\frac{1}{5}}\right).\sqrt{5}$ | $ \begin{array}{l}\left(3\sqrt{20}-\sqrt{125}-15\sqrt{\frac{1}{5}}\right).\sqrt{5}\\ =\left(3\sqrt{4.5}-\sqrt{25.5}-\frac{15}{\sqrt{5}}\right).\sqrt{5}\\ =\left(6\sqrt{5}-5\sqrt{5}-\frac{15}{\sqrt{5}}\right).\sqrt{5}\\ =\sqrt{5}.\sqrt{5}-\text{\hspace{0.17em}}\frac{15}{\sqrt{5}}.\sqrt{5}=5-15=-10\end{array}$ | https://khoahoc.vietjack.com/question/1009101 | ### Câu hỏi:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><msqrt><mn>20</mn></msqrt><mo>−</mo><msqrt><mn>125</mn></msqrt><mo>−</mo><mn>15</mn><msqrt><mfrac><mn>1</mn><mn>5</mn></mfrac></msqrt></mrow></mfenced><mo>.</mo><msqrt><mn>5</mn></msqrt></math>
### Lời giải:
<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mn>3</mn><msqrt><mn>20</mn></msqrt><mo>−</mo><msqrt><mn>125</mn></msqrt><mo>−</mo><mn>15</mn><msqrt><mfrac><mn>1</mn><mn>5</mn></mfrac></msqrt></mrow></mfenced><mo>.</mo><msqrt><mn>5</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><msqrt><mn>4.5</mn></msqrt><mo>−</mo><msqrt><mn>25.5</mn></msqrt><mo>−</mo><mfrac><mn>15</mn><msqrt><mn>5</mn></msqrt></mfrac></mrow></mfenced><mo>.</mo><msqrt><mn>5</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>6</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>5</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mfrac><mn>15</mn><msqrt><mn>5</mn></msqrt></mfrac></mrow></mfenced><mo>.</mo><msqrt><mn>5</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>.</mo><msqrt><mn>5</mn></msqrt><mo>−</mo><mtext> </mtext><mfrac><mn>15</mn><msqrt><mn>5</mn></msqrt></mfrac><mo>.</mo><msqrt><mn>5</mn></msqrt><mo>=</mo><mn>5</mn><mo>−</mo><mn>15</mn><mo>=</mo><mo>−</mo><mn>10</mn></mtd></mtr></mtable></math>
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