# How do you simplify: square root (3/ 5)?

Jul 26, 2015

Using $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ for $a \ge 0$ and $b > 0$

$\sqrt{\frac{3}{5}} = \sqrt{\frac{3 \cdot 5}{5 \cdot 5}} = \frac{\sqrt{3 \cdot 5}}{\sqrt{5 \cdot 5}} = \frac{\sqrt{15}}{5}$

#### Explanation:

We could also do it the other way:

$\sqrt{\frac{3}{5}} = \frac{\sqrt{3}}{\sqrt{5}}$

$= \frac{\sqrt{3}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

$= \frac{\sqrt{3} \sqrt{5}}{\sqrt{5} \sqrt{5}}$

$= \frac{\sqrt{15}}{5}$

using $\sqrt{a} \sqrt{b} = \sqrt{a b}$ when $a , b \ge 0$