# How do you simplify sqrt(5/4 )+ sqrt(10/8)?

Sep 2, 2016

$\sqrt{5}$

#### Explanation:

Split the root so there is a separate numerator and denominator.

$\frac{\sqrt{5}}{\sqrt{4}} + \frac{\sqrt{10}}{\sqrt{4 \times 2}}$

=$\frac{\sqrt{5}}{2} + \frac{\sqrt{10}}{2 \sqrt{2}} \text{ find LCD}$

=$\frac{\textcolor{red}{\sqrt{2} \times \sqrt{5}} + \sqrt{10}}{2 \sqrt{2}}$

=$\frac{\textcolor{red}{\sqrt{10}} + \sqrt{10}}{2 \sqrt{2}}$

=$\frac{\cancel{2} \sqrt{10}}{\cancel{2} \sqrt{2}}$

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

=$\sqrt{5}$

Nice!!