# How do you simplify sqrt5/(5+sqrt2)?

May 30, 2017

See below.

#### Explanation:

To simplify, we have to multiply by the conjugate of the denominator, or $5 - \sqrt{2}$.

$\frac{\sqrt{5}}{5 + \sqrt{2}} \setminus \cdot \frac{5 - \sqrt{2}}{5 - \sqrt{2}} = \frac{5 \sqrt{5} - \sqrt{10}}{25 - 2} = \frac{5 \sqrt{5} - \sqrt{10}}{23}$