Find the square root.-sqrtfrac{9}{25}=

Question

Find the square root.
$- \sqrt{\frac{9}{25}} =$

Answer 1

The quotient rule for roots is

\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}

.Using this rule gives:

- \sqrt{\frac{9}{25}} = - \frac{\sqrt{9}}{\sqrt{25}}

To simplify the roots, we need to use the rule

\sqrt{x^{2}} = x

when x>0. Since

9 = 3^{3}

, then

\sqrt{9} = {{\sqrt{3}}^{2}} = 3

. Since

25 = 5^{2}

, then

\sqrt{25} = \sqrt{5^{2}} = 5

. Therefore

- \frac{\sqrt{9}}{\sqrt{25}} = - \frac{3}{5}

Expert Answer