# How do you simplify 12 (sqrt of 2) divided by 2 (sqrt of 27)?

Oct 9, 2015

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

#### Explanation:

Assuming that your starting expression looks like this

$\frac{12 \sqrt{2}}{2 \sqrt{27}}$

you can start by writing

$\frac{12 \sqrt{2}}{2 \sqrt{27}} = \frac{6 \sqrt{2}}{\sqrt{27}}$

Now focus on $\sqrt{27}$. Notice that you can write $27$ as

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

This means that you have

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

The expression becomes

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

Rationalize the denominator by multiplying the fraction by $1 = \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{2 \sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{2 \cdot \sqrt{2} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \textcolor{g r e e n}{\frac{2}{3} \sqrt{6}}$