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Pre-algebra

Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

$Math Studyset 91影视 Explanations$ Math

Common Core Edition 路 183 pages

ISBN: 9780547587776

Chapter 9: Q4. (page 483)

Simplify the expression.
$\sqrt{\frac{32}{n^{2}}}$

Short Answer

Expert verified

The simplified value is $\frac{4 \sqrt{2}}{n}$ .

Step by step solution

01

Step 1. Given Information.

The given expression is $\sqrt{\frac{32}{n^{2}}}$ .

02

Step 2. Calculation.

The expression can be simplified as,

$\begin{matrix} \sqrt{\frac{32}{n^{2}}} = \frac{\sqrt{32}}{\sqrt{n^{2}}} \\ = \frac{{(32)}^{\frac{1}{2}}}{{(n^{2})}^{\frac{1}{2}}} \\ = {\frac{(2 脳 2 脳 2 脳 2 脳 2)}{n}}^{\frac{1}{2}} \\ = \frac{2 脳 2 \sqrt{2}}{n} \end{matrix}$

On further simplification,

$\frac{2 脳 2 \sqrt{2}}{n} = \frac{4 \sqrt{2}}{n}$

03

Step 3. Conclusion.

The simplified value of the given expression is $\frac{4 \sqrt{2}}{n}$ .

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