# How do you simplify (6sqrt3)/sqrt5?

Jun 9, 2018

(6sqrt3)/sqrt5=color(blue)((6sqrt15)/5

#### Explanation:

Simplify:

$\frac{6 \sqrt{3}}{\sqrt{5}}$

First rationalize the denominator by multiplying both the numerator and the denominator by $\sqrt{5}$.

$\frac{6 \sqrt{3} \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Apply rule: $\sqrt{a} \sqrt{a} = a$

$\frac{6 \sqrt{3} \sqrt{5}}{5}$

Apply rule: $\sqrt{a} \sqrt{b} = \sqrt{a b}$

$\frac{6 \sqrt{15}}{5}$