# How do you simplify sqrt2 div 5sqrt3?

Nov 10, 2015

$\frac{\sqrt{\frac{2}{3}}}{5}$

#### Explanation:

Step 1: Rewrite in fraction form:
$\frac{\sqrt{2}}{5 \sqrt{3}}$

Then you can separate the square roots from the fraction:
$\frac{1}{5} \cdot \frac{\sqrt{2}}{\sqrt{3}}$

When a fraction has the same exponent (in this case $\frac{1}{2}$) you can rewrite the exponent outside of the entire fraction like this:

$\frac{1}{5} \cdot {\left(\frac{2}{3}\right)}^{\frac{1}{2}}$ or $\frac{1}{5} \cdot \sqrt{\frac{2}{3}}$

At this point you can accept the previus answers as the simplified form or you can remove the $\frac{1}{5}$ and instead, put the entire root divided by 5:
$\frac{\sqrt{\frac{2}{3}}}{5}$