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

Mar 25, 2018

$\implies 2 \sqrt{2} i$

#### Explanation:

$\implies \frac{\sqrt{- 16}}{\sqrt{2}}$

We can combine the square root:

$\implies \sqrt{- \frac{16}{2}}$

Dividing the argument of the root:

$\implies \sqrt{- 8}$

We can find factors to potentially pull out of the square root.

$\implies \sqrt{2 \times 4 \times {i}^{2}}$

Simplifying:

$\implies 2 \sqrt{2} i$