Simplify square root of 8/(x^2)

$\sqrt{\frac{8}{x^{2}}}$

Step 1

Rewrite $\frac{8}{x^{2}}$ as ${(\frac{2}{x})}^{2} \cdot 2$ .

Factor the perfect power $2^{2}$ out of $8$ .

$\sqrt{\frac{2^{2} \cdot 2}{x^{2}}}$

Factor the perfect power $x^{2}$ out of $x^{2}$ .

$\sqrt{\frac{2^{2} \cdot 2}{x^{2} \cdot 1}}$

Rearrange the fraction $\frac{2^{2} \cdot 2}{x^{2} \cdot 1}$ .

$\sqrt{{(\frac{2}{x})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$\frac{2}{x} \sqrt{2}$

Step 3

Combine $\frac{2}{x}$ and $\sqrt{2}$ .

$\frac{2 \sqrt{2}}{x}$