# How do you simplify sqrt(-100) + 9sqrt(-4)?

Dec 4, 2015

$28 i$

#### Explanation:

$\sqrt{- 100} + 9 \sqrt{- 4}$
$= \sqrt{- 1 \times {10}^{2}} + 9 \sqrt{- 1 \times {2}^{2}}$
$= \sqrt{- 1} \sqrt{{10}^{2}} + 9 \sqrt{- 1} \sqrt{{2}^{2}}$

Recall that $\sqrt{- 1} = i$ and that $\sqrt{{a}^{2}} = a$.

$= 10 i + 18 i$
$= 28 i$