# How do you simplify  3 /sqrt18?

Apr 3, 2016

$\frac{\sqrt{2}}{2}$

#### Explanation:

Turn $18$ into a surd form, by looking at its factors and identifying square numbers and doing the following

$\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3 \sqrt{2}$
$\therefore \sqrt{18} = 3 \sqrt{2}$

Now substitute that into the fraction and simplify by cancelling out the $3$'s.

$\frac{3}{\sqrt{18}} = \frac{3}{3 \sqrt{2}} = \frac{1}{\sqrt{2}}$

Rationalise the denominator, or make it not a square root by multiplying by $\frac{\sqrt{2}}{\sqrt{2}}$.

$\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2}$