Summarize this article in one sentence.
These are the numbers outside of the radical sign. To simplify them, divide or reduce, ignoring the square roots for now. For example, if you are calculating 432616{\displaystyle {
rac {4{\sqrt {32}}}{6{\sqrt {16}}}}}, you would first simplify 46{\displaystyle {
rac {4}{6}}}. The numerator and denominator can both be divided by a factor of 2. So, you can reduce: 46=23{\displaystyle {
rac {4}{6}}={
rac {2}{3}}}. . If the numerator is evenly divisible by the denominator, simply divide the radicands. If not, simplify each square root as you would any square root. For example, since 32 is evenly divisible by 16, you can divide the square roots:3216=2{\displaystyle {\sqrt {
rac {32}{16}}}={\sqrt {2}}}. Remember that you cannot have a square root in a denominator, so when multiplying a fraction by a square root, place the square root in the numerator. For example, 232=223{\displaystyle {
rac {2}{3}} imes {\sqrt {2}}={
rac {2{\sqrt {2}}}{3}}}. This is called rationalizing the denominator. As a rule, an expression cannot have a square root in the denominator. To rationalize the denominator, multiply the numerator and denominator by the square root you need to cancel. For example, if your expression is 4327{\displaystyle {
rac {4{\sqrt {3}}}{2{\sqrt {7}}}}}, you need to multiply the numerator and denominator by 7{\displaystyle {\sqrt {7}}} to cancel the square root in the denominator:43777{\displaystyle {
rac {4{\sqrt {3}}}{\sqrt {7}}} imes {
rac {\sqrt {7}}{\sqrt {7}}}}=43777{\displaystyle ={
rac {4{\sqrt {3}} imes {\sqrt {7}}}{{\sqrt {7}} imes {\sqrt {7}}}}}=42149{\displaystyle ={
rac {4{\sqrt {21}}}{\sqrt {49}}}}=4217{\displaystyle ={
rac {4{\sqrt {21}}}{7}}}
Simplify the coefficients. Simplify the square roots Multiply the simplified coefficient(s) by the simplified square root. Cancel the square root in the denominator, if necessary.