Chapter 8.2, Problem 9CE

To determine

To Simplify: Simplify the given expression

Answer to Problem 9CE

The simplified form is ${\left(\frac{3}{\sqrt{5}}\right)}^2=\frac{9}{5}$

Explanation of Solution

Given information: The given expression is ${\left(\frac{3}{\sqrt{5}}\right)}^2$

We have the given expression is ${\left(\frac{3}{\sqrt{5}}\right)}^2$

It can be further written as

  $\begin{array}{c}{\left(\frac{3}{\sqrt{5}}\right)}^2=\left(\frac{3}{\sqrt{5}}\right)\left(\frac{3}{\sqrt{5}}\right)\\ =\left(\frac{3^2}{\sqrt{5}\sqrt{5}}\right)\\ =\left(\frac{9}{\sqrt{5^2}}\right)\\ =\left(\frac{9}{5}\right)\end{array}$

Since square root is positive quantity so we neglect negative sign.

Therefore, the simplified form is ${\left(\frac{3}{\sqrt{5}}\right)}^2=\frac{9}{5}$