# How do you simplify 7sqrt(-36) + 4sqrt(-81)?

Nov 15, 2015

0

#### Explanation:

$\sqrt{\text{-36}}$ = 0
$\sqrt{\text{-81}}$ = 0
The square root of a negative integer = 0
(7$\times$0) + (4$\times$0) = 0

Nov 15, 2015

$78 i$

#### Explanation:

If $x \in \mathbb{R} \mathmr{and} x > 0$, then $\sqrt{- x} = i \sqrt{x}$, where ${i}^{2} = - 1 \mathmr{and} i = \sqrt{- 1} \in \mathbb{C}$.

Therefore,

$7 \sqrt{- 36} + 4 \sqrt{- 81} = 7 \cdot \left(6 i\right) + 4 \cdot \left(9 i\right)$

$= 42 i + 36 i$

$= 78 i$