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Q12.

Expert-verified
Found in: Page 291

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# Simplify each expression.${\left(\frac{2}{3}\sqrt{6}\right)}^{2}$

The simplified form is,

${\left(\frac{2}{3}\sqrt{6}\right)}^{2}=\frac{8}{3}$.

See the step by step solution

## Step 1. Given information.

The given expression is,

${\left(\frac{2}{3}\sqrt{6}\right)}^{2}$.

## Step 2. It can be further written as below.

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

Then,

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

## Step 3. Neglect negative sign.

Since, square root is positive quantity

So, we neglect negative sign.

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