# How do you simplify sqrt(3/(27y^6))?

Sep 25, 2015

$\textcolor{red}{\sqrt{\frac{3}{27 {y}^{6}}} = \frac{1}{3 {y}^{3}}}$

#### Explanation:

First divide the numerator and denominator by $3$.

$\sqrt{\frac{3}{27 {y}^{6}}} = \sqrt{\frac{1}{9 {y}^{6}}}$

Remember that $\sqrt{{x}^{n}} = {x}^{\frac{n}{2}}$

So $\sqrt{{y}^{6}} = {y}^{\frac{6}{2}} = {y}^{3}$ and

$\sqrt{\frac{1}{9 {y}^{6}}} = \frac{1}{3 {y}^{3}}$

$\sqrt{\frac{3}{27 {y}^{6}}} = \frac{1}{3 {y}^{3}}$