# What is sqrt(27/16)?

Jul 26, 2015

#### Answer:

I found: $\frac{3}{4} \sqrt{3}$

#### Explanation:

You can write your square root as:
$\frac{\sqrt{27}}{\sqrt{16}} = \frac{\sqrt{3 \cdot 9}}{4} = \frac{\sqrt{9} \sqrt{3}}{4} = \frac{3}{4} \sqrt{3}$

Jul 26, 2015

#### Answer:

$\frac{3 \sqrt{3}}{4}$

#### Explanation:

Use the quotient property of radicals to rewrite your expression as

$\sqrt{\frac{27}{16}} = \frac{\sqrt{27}}{\sqrt{16}} = \frac{\sqrt{27}}{4}$

Since $27$ is not a perfect square, you're going to have to see if you can write it as a product of a perfect square and another number

$27 = 9 \cdot 3 = {3}^{2} \cdot 3$

This means that your expression will be

$\frac{\sqrt{{3}^{2} \cdot 3}}{4} = \frac{\sqrt{{3}^{2}} \cdot \sqrt{3}}{4} = \textcolor{g r e e n}{\frac{3 \sqrt{3}}{4}}$