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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 8: Q12. (page 291)

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

Short Answer

Expert verified

The simplified form is,

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

Step by step solution

01

Step 1. Given information.

The given expression is,

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

02

Step 2. It can be further written as below.

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

Then,

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

03

Step 3. Neglect negative sign.

Since, square root is positive quantity

So, we neglect negative sign.

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

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