Question

Simplify the expression.

$\sqrt{\frac{32}{n^2}}$

Short answer

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

Step-by-step solution

Step 1. Given Information.

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

Step 2. Calculation.

The expression can be simplified as,

$\begin{array}{c}\sqrt{\frac{32}{n^2}}=\frac{\sqrt{32}}{\sqrt{n^2}}\\ =\frac{{\left(32\right)}^{\frac{1}{2}}}{{\left(n^2\right)}^{\frac{1}{2}}}\\ ={\frac{(2\times 2\times 2\times 2\times 2)}{n}}^{\frac{1}{2}}\\ =\frac{2\times 2\sqrt{2}}{n}\end{array}$

On further simplification,

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

Step 3. Conclusion.

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