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

Oct 16, 2015

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

#### Explanation:

$\frac{4}{\sqrt{5} + \sqrt{5}}$

Notice that you can combine the two radical terms in the denominator to get

$\sqrt{5} + \sqrt{5} = \sqrt{5} \cdot \left(1 + 1\right) = 2 \sqrt{5}$

The expression becomes

$\frac{4}{2 \sqrt{5}} = \frac{2}{\sqrt{5}}$

Next, rationalize the denominator by multiplyg the fraction by $1 = \frac{\sqrt{5}}{\sqrt{5}}$. This will get you

$\frac{2}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{2 \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \textcolor{g r e e n}{\frac{2 \sqrt{5}}{5}}$