# How do you simplify (8sqrt3)/sqrt6?

Mar 22, 2018

$4 \sqrt{2}$

#### Explanation:

First we need to rationalize the denominator (no radicals can be in a denominator)

$\frac{8 \sqrt{3}}{\sqrt{6}} \rightarrow$ Multiply the numerator and denominator by $\sqrt{6}$ to get rid of the radical

$\frac{8 \sqrt{18}}{6}$

$\frac{8 \sqrt{9} \cdot \sqrt{2}}{6} \rightarrow$ 9 is a perfect square

$\frac{8 \cdot 3 \cdot \sqrt{2}}{6}$

$\frac{24 \sqrt{2}}{6} \rightarrow$ 24 is divisible by 6

$4 \sqrt{2}$