# How do you simplify sqrt2/sqrt6?

Feb 7, 2017

Rationalize the denominator to get $\frac{\sqrt{3}}{3}$

#### Explanation:

Start by multiplying the fraction by $\frac{\sqrt{6}}{\sqrt{6}}$,

(sqrt6xxsqrt2)/(sqrt6xxsqrt6" " Simplify to get

$\frac{\sqrt{12}}{6}$

$= \frac{\sqrt{4} \times \sqrt{3}}{6} \text{ }$ Finally, work out $\sqrt{4}$ in the numerator:

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

Remember that $\frac{\sqrt{x}}{\sqrt{y}} = \frac{\sqrt{x y}}{y}$