# How do you simplify sqrt(6)/(4+sqrt(2))?

Mar 3, 2016

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

#### Explanation:

The idea is to rationalise the denominator, we can do this by multiplying the top and the bottom of the fraction by the conjugate of the bottom:

$\frac{4 - \sqrt{2}}{4 - \sqrt{2}}$

We have just took the negative of the square root term.

Now:

$\frac{\sqrt{6}}{4 + \sqrt{2}} \cdot \frac{4 - \sqrt{2}}{4 - \sqrt{2}}$

=(4sqrt(6)-sqrt2*sqrt6)/(16+4sqrt(2)-4sqrt(2)-2

$= \frac{4 \sqrt{6} - \sqrt{12}}{14}$

Transform the $\sqrt{12}$ term into a surd like so:

$= \frac{4 \sqrt{6} - 2 \sqrt{3}}{14} = \frac{2 \sqrt{6} - \sqrt{3}}{7}$