# How do you simplify 2sqrt(-16/7)?

Dec 13, 2015

$\frac{8 \sqrt{7} i}{7}$

#### Explanation:

This can be rewritten as

$2 \sqrt{- 1 \times \frac{16}{7}}$

$= 2 i \sqrt{\frac{16}{7}}$

$= \frac{2 i \sqrt{16}}{\sqrt{7}}$

$= \frac{8 i}{\sqrt{7}}$

$= \frac{8 i}{\sqrt{7}} \left(\frac{\sqrt{7}}{\sqrt{7}}\right)$

$= \frac{8 \sqrt{7} i}{7}$

Notice that the $i$ is not included in the square root in the final answer.