# How do you simplify (sqrt5+sqrt2)/sqrt10?

Sep 7, 2016

$\frac{\sqrt{5} + \sqrt{2}}{\sqrt{10}}$

= $\frac{\sqrt{2}}{2} + \frac{\sqrt{5}}{5}$

#### Explanation:

To simplify $\frac{\sqrt{5} + \sqrt{2}}{\sqrt{10}}$, we need to rationalize denominator.

As it is $\sqrt{10}$, $\frac{\sqrt{5} + \sqrt{2}}{\sqrt{10}}$ can be rationalized by multiplying numerator and denominator by $\sqrt{10}$.

Hence $\frac{\sqrt{5} + \sqrt{2}}{\sqrt{10}}$

= $\frac{\sqrt{10} \left(\sqrt{5} + \sqrt{2}\right)}{\sqrt{10}} ^ 2$

= $\frac{\sqrt{50} + \sqrt{20}}{10}$

= (sqrt(2×5×5)+sqrt(2×2×5))/10

= $\frac{5 \sqrt{2} + 2 \sqrt{5}}{10}$

= $\frac{\sqrt{2}}{2} + \frac{\sqrt{5}}{5}$