# How do you simplify sqrt(5/7)*sqrt(2/5)?

Sep 29, 2015

$\frac{\sqrt{14}}{7}$

#### Explanation:

Since the two radicals have the same index 2, you can combine them under one radical symbol.

$\sqrt{\frac{5}{7}} \cdot \sqrt{\frac{2}{5}}$
$= \sqrt{\frac{\cancel{5}}{7} \cdot \frac{2}{\cancel{5}}}$
$= \sqrt{\frac{2}{7}}$

You can leave it there, or you can continue by rationalizing it. To rationalize it, you have to take out the denominator out of the radical symbol.

$\sqrt{\frac{2}{7}}$
$= \sqrt{\frac{2}{7} \cdot \frac{7}{7}}$
$= \sqrt{\frac{2 \cdot 7}{7} ^ 2}$
$= \frac{\sqrt{2 \cdot 7}}{7}$
$\textcolor{b l u e}{= \frac{\sqrt{14}}{7}}$