# What is the square root of (x^6)/27?

Jul 18, 2015

$\sqrt{\frac{{x}^{6}}{27}} = \frac{\sqrt{3}}{9} \left\mid {x}^{3} \right\mid$

#### Explanation:

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$ and $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

$\sqrt{\frac{{x}^{6}}{27}} = \sqrt{\frac{3 {x}^{6}}{81}} = \frac{\sqrt{{x}^{6}} \sqrt{3}}{\sqrt{81}} = \frac{\left\mid {x}^{3} \right\mid \sqrt{3}}{9} = \frac{\sqrt{3}}{9} \left\mid {x}^{3} \right\mid$

Note $\left\mid {x}^{3} \right\mid$, not ${x}^{3}$.

If $x < 0$ then ${x}^{3} < 0$, but $\sqrt{{x}^{6}} > 0$ since sqrt denotes the positive square root.