# How do you simplify 6√2 divided by √3?

Sep 6, 2015

$\frac{6 \sqrt{2}}{\sqrt{3}} = 2 \sqrt{6}$

#### Explanation:

Start by rationalizing the denominator. That can be done by multiplying the fraction by $1 = \frac{\sqrt{3}}{\sqrt{3}}$.

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

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

$= \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} 2 \sqrt{6}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \textcolor{g r e e n}{2 \sqrt{6}}$