Simplify - square root of -25

$- \sqrt{- 25}$

Step 1

Rewrite $- 25$ as $- 1 (25)$ .

$- \sqrt{- 1 (25)}$

Step 2

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$- (\sqrt{- 1} \cdot \sqrt{25})$

Step 3

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

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

Step 4

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

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

Step 5

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

$- (i \cdot 5)$

Step 6

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

$- (5 \cdot i)$

Step 7

Multiply $5$ by $- 1$ .

$- 5 i$