# How do you simplify 36/sqrt15?

Jul 4, 2017

$\frac{36}{\sqrt{15}} = \frac{12 \sqrt{15}}{5}$

#### Explanation:

$\frac{36}{\sqrt{15}}$

= $\frac{36}{\sqrt{15}} \times \frac{\sqrt{15}}{\sqrt{15}}$

= $\frac{36 \times \sqrt{15}}{\sqrt{15} \times \sqrt{15}}$

= $\frac{36 \times \sqrt{15}}{15}$

= $\frac{{\cancel{36}}^{12} \times \sqrt{15}}{{\cancel{15}}^{5}}$

= $\frac{12 \sqrt{15}}{5}$

Jul 4, 2017

$\frac{12 \sqrt{15}}{5}$

#### Explanation:

To simplify a fraction with a radical, we want to make sure that there is no radical on the bottom. In order to do this, we can multiply the fraction by $\frac{\sqrt{15}}{\sqrt{15}}$"

$\frac{36}{\sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}}$

$= \frac{36 \cdot \sqrt{15}}{\sqrt{15} \cdot \sqrt{15}}$

$= \frac{36 \sqrt{15}}{15}$

We have one last step to simplify this expression. Notice that the top and bottom both share a factor of 3 now. So, we need to divide both the top and bottom by 3:

$\frac{36 \sqrt{15}}{15} \div \frac{3}{3}$

$= \frac{36 \sqrt{15} \div 3}{15 \div 3}$

$= \frac{12 \sqrt{15}}{5}$