Simplify square root of -125

$\sqrt{- 125}$

Step 1

Rewrite $- 125$ as $- 1 (125)$ .

$\sqrt{- 1 (125)}$

Step 2

Rewrite $\sqrt{- 1 (125)}$ as $\sqrt{- 1} \cdot \sqrt{125}$ .

$\sqrt{- 1} \cdot \sqrt{125}$

Step 3

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

$i \cdot \sqrt{125}$

Step 4

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$i \cdot \sqrt{25 (5)}$

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

$i \cdot \sqrt{5^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

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

Step 6

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

$5 i \sqrt{5}$