Simplify – square root of -100

$- \sqrt{- 100}$

Rewrite $- 100$ as $- 1 (100)$ .

$- \sqrt{- 1 (100)}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$- (\sqrt{- 1} \cdot \sqrt{100})$

Rewrite $\sqrt{- 1}$ as $i$ .

$- (i \cdot \sqrt{100})$

Rewrite $100$ as $10^{2}$ .

$- (i \cdot \sqrt{10^{2}})$

Pull terms out from under the radical, assuming positive real numbers.

$- (i \cdot 10)$

Move $10$ to the left of $i$ .

$- (10 \cdot i)$

Multiply $10$ by $- 1$ .

$- 10 i$

Simplify – square root of -100

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