Chapter 8.2, Problem 12CE

To determine

To Simplify: Simplify the given expression

Answer to Problem 12CE

The simplified form is ${\left(\frac{2}{3}\sqrt{6}\right)}^2=\frac{8}{3}$

Explanation of Solution

Given information: The given expression is ${\left(\frac{2}{3}\sqrt{6}\right)}^2$

We have the given expression is ${\left(\frac{2}{3}\sqrt{6}\right)}^2$

It can be further written as

  $\begin{array}{c}{\left(\frac{2}{3}\sqrt{6}\right)}^2=\left(\frac{2}{3}\sqrt{6}\right)\left(\frac{2}{3}\sqrt{6}\right)\\ =\left(\frac{2^2}{3^2}\sqrt{6}.\sqrt{6}\right)\\ =\left(\frac{4}{9}\sqrt{6^2}\right)\\ =\frac{4}{9}\times 6\\ =\frac{4}{3}\times 2\\ =\frac{8}{3}\end{array}$

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

Therefore, the simplified form is ${\left(\frac{2}{3}\sqrt{6}\right)}^2=\frac{8}{3}$