# How do you simplify the square root of -8/9?

May 10, 2018

$\sqrt{- \frac{8}{9}} = \frac{2}{3} \sqrt{2} i$

#### Explanation:

You want to know $\sqrt{- \frac{8}{9}}$

We note that $8 = {2}^{3}$ and $9 = {3}^{2}$, and also $\sqrt{- 1} = i$

Therefore
$\sqrt{- \frac{8}{9}} = \sqrt{- 1 \cdot {2}^{3} / {3}^{2}}$
$= \frac{\sqrt{{2}^{3}}}{\sqrt{{3}^{2}}} \sqrt{- 1}$
$= \frac{2}{3} \sqrt{2} i$