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Q12.

Expert-verified

Geometry

Found in: Page 291

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

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

The simplified form is,

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given expression is,

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

Step 2. It can be further written as below.

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

Then,

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

Step 3. Neglect negative sign.

Since, square root is positive quantity

So, we neglect negative sign.

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

Most popular questions for Math Textbooks

Simplify each expression.

${(\frac{n}{\sqrt{3}})}^{2}$

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Refer to the figure at the right.

If $J M = 3$ and $M K = 6$ , find $L M$ .

Find the value of $x$ from the given figure.

Simplify

$\sqrt{225}$

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