Simplify square root of -175

$\sqrt{- 175}$

Step 1

Rewrite $- 175$ as $- 1 (175)$ .

$\sqrt{- 1 (175)}$

Step 2

Rewrite $\sqrt{- 1 (175)}$ as $\sqrt{- 1} \cdot \sqrt{175}$ .

$\sqrt{- 1} \cdot \sqrt{175}$

Step 3

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

$i \cdot \sqrt{175}$

Step 4

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$i \cdot \sqrt{25 (7)}$

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

$i \cdot \sqrt{5^{2} \cdot 7}$

Step 5

Pull terms out from under the radical.

$i \cdot (5 \sqrt{7})$

Step 6

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

$5 i \sqrt{7}$