Simplify square root of 8/(x^6)

$\sqrt{\frac{8}{x^{6}}}$

Step 1

Rewrite $\frac{8}{x^{6}}$ as ${(\frac{2}{x^{3}})}^{2} \cdot 2$ .

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

$\sqrt{\frac{2^{2} \cdot 2}{x^{6}}}$

Factor the perfect power ${(x^{3})}^{2}$ out of $x^{6}$ .

$\sqrt{\frac{2^{2} \cdot 2}{{(x^{3})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{2^{2} \cdot 2}{{(x^{3})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{2}{x^{3}})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$\frac{2}{x^{3}} \sqrt{2}$

Step 3

Combine $\frac{2}{x^{3}}$ and $\sqrt{2}$ .

$\frac{2 \sqrt{2}}{x^{3}}$