Simplify - square root of -50

$- \sqrt{- 50}$

Step 1

Rewrite $- 50$ as $- 1 (50)$ .

$- \sqrt{- 1 (50)}$

Step 2

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$- (\sqrt{- 1} \cdot \sqrt{50})$

Step 3

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

$- (i \cdot \sqrt{50})$

Step 4

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$- (i \cdot \sqrt{25 (2)})$

Rewrite $25$ as $5^{2}$ .

$- (i \cdot \sqrt{5^{2} \cdot 2})$

Step 5

Pull terms out from under the radical.

$- (i \cdot (5 \sqrt{2}))$

Step 6

Simplify the expression.

Move $5$ to the left of $i$ .

$- (5 \cdot i \sqrt{2})$

Multiply $5$ by $- 1$ .

$- 5 i \sqrt{2}$