# How do you simplify  sqrt ((2x)/(9x))?

Apr 30, 2016

$\sqrt{\frac{2 x}{9 x}} = \frac{\sqrt{2}}{3}$ excluding $x = 0$

#### Explanation:

For any positive Real numbers $a , b$:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

So we find:

$\sqrt{\frac{2 \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}}}{9 \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}}}} = \sqrt{\frac{2}{3} ^ 2} = \frac{\sqrt{2}}{\sqrt{{3}^{2}}} = \frac{\sqrt{2}}{3}$

excluding $x = 0$, when $\sqrt{\frac{2 x}{9 x}} = \sqrt{\frac{0}{0}}$ is undefined.