Simplify - square root of -100

$- \sqrt{- 100}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

$- (i \cdot 10)$

Step 6

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

$- (10 \cdot i)$

Step 7

Multiply $10$ by $- 1$ .

$- 10 i$