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If your expression is not already set up like a fraction, rewrite it this way. This makes it easier to follow all the necessary steps when dividing by a square root. Remember that a fraction bar is also a division bar. For example, if you are calculating 14436{\displaystyle {\sqrt {144}}\div {\sqrt {36}}}, rewrite the problem like this: 14436{\displaystyle {
rac {\sqrt {144}}{\sqrt {36}}}}. If your problem has a square root in the numerator and denominator, you can place both radicands under one radical sign. (A radicand is a number under a radical, or square root, sign.) This will simplify the simplifying process. For example, 14436{\displaystyle {
rac {\sqrt {144}}{\sqrt {36}}}} can be rewritten as 14436{\displaystyle {\sqrt {
rac {144}{36}}}}. Divide the numbers as you would any whole number. Make sure to place their quotient under a new radical sign. For example, 14436=4{\displaystyle {
rac {144}{36}}=4}, so 14436=4{\displaystyle {\sqrt {
rac {144}{36}}}={\sqrt {4}}}. , if necessary. If the radicand is a perfect square, or if one of its factors is a perfect square, you need to simplify the expression. A perfect square is the product of a whole number multiplied by itself. For example, 25 is a perfect square, since 55=25{\displaystyle 5 imes 5=25}. For example, 4 is a perfect square, since 22=4{\displaystyle 2 imes 2=4}. Thus:4{\displaystyle {\sqrt {4}}}=22{\displaystyle ={\sqrt {2 imes 2}}}=2{\displaystyle =2}So, 14436=4=2{\displaystyle {
rac {\sqrt {144}}{\sqrt {36}}}={\sqrt {4}}=2}.
Set up a fraction. Use one radical sign. Divide the radicands. Simplify