# How do you rationalize the denominator and simplify sqrt(5/3)?

Jun 18, 2018

$\frac{\sqrt{15}}{3}$

#### Explanation:

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

use the rule: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

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

now multiply by 1 in the form $\frac{a}{a}$ to rationalize:

$\frac{\sqrt{5}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{15}}{\sqrt{9}} = \frac{\sqrt{15}}{3}$

Jun 18, 2018

$\frac{\sqrt{15}}{3}$

#### Explanation:

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

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

$\Rightarrow = \frac{\sqrt{15}}{\sqrt{9}}$

$\Rightarrow \frac{\sqrt{15}}{3}$