# How do you simplify sqrt(–(–7)^2)?

Apr 17, 2018

$\implies 7 i$

#### Explanation:

$\sqrt{- {\left(- 7\right)}^{2}}$

$= \sqrt{- 49}$

$= \sqrt{\left(49\right) \cdot \left(- 1\right)}$

$= \sqrt{49} \cdot \sqrt{- 1}$

$= \sqrt{{7}^{2}} \cdot \sqrt{- 1}$

$= \left(7\right) \cdot \left(i\right)$

$= 7 i$

Apr 17, 2018

$\sqrt{- {\left(- 7\right)}^{2}} = \pm 7 i$
$\sqrt{- {\left(- 7\right)}^{2}} = \sqrt{- 49} = \sqrt{- 1} \sqrt{49} = \pm i 7 = \pm 7 i$
Over $\mathbb{R}$, we would only take the positive square root of $\sqrt{{a}^{2}}$, but the square root function is multi-variable over $\mathbb{C}$, so we take both roots.