# How do you simplify sqrt2/(2sqrt3)?

Aug 13, 2016

$\frac{1}{\sqrt{6}}$

#### Explanation:

Can write $2 = \sqrt{2} \sqrt{2}$

$\frac{\sqrt{2}}{\sqrt{2} \sqrt{2} \sqrt{3}} = \frac{1}{\sqrt{2} \sqrt{3}} = \frac{1}{\sqrt{6}}$

Aug 13, 2016

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

#### Explanation:

It is generally not good practice to leave a radical in the denominator so we try to change the denominator into a rational number.

This is called rationalising the denominator.

$\frac{\sqrt{2}}{2 \sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \text{ } \frac{\sqrt{3}}{\sqrt{3}} = 1$

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

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