Evaluate square root of -75

$\sqrt{- 75}$

Step 1

Rewrite $- 75$ as $- 1 (75)$ .

$\sqrt{- 1 (75)}$

Step 2

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$\sqrt{- 1} \cdot \sqrt{75}$

Step 3

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

$i \cdot \sqrt{75}$

Step 4

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$i \cdot \sqrt{25 (3)}$

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

$i \cdot \sqrt{5^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$i \cdot (5 \sqrt{3})$

Step 6

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

$5 i \sqrt{3}$