# How do you rationalize the denominator and simplify sqrt5/sqrt19?

Sep 7, 2017

$\frac{\sqrt{5}}{\sqrt{19}} = \frac{\sqrt{95}}{19}$

#### Explanation:

Simplify:

$\frac{\sqrt{5}}{\sqrt{19}}$

Rationalize the denominator by multiplying the numerator and denominator by $\sqrt{19}$.

$\frac{\sqrt{5} \cdot \sqrt{19}}{\sqrt{19} \cdot \sqrt{19}}$

Simplify.

$\frac{\sqrt{5} \cdot \sqrt{19}}{19}$

Apply the rule: $a \ge \sqrt{a} \cdot \sqrt{b} = \sqrt{a b}$.

$\frac{\sqrt{95}}{19}$