Simplify square root of -252

$\sqrt{- 252}$

Step 1

Rewrite $- 252$ as $- 1 (252)$ .

$\sqrt{- 1 (252)}$

Step 2

Rewrite $\sqrt{- 1 (252)}$ as $\sqrt{- 1} \cdot \sqrt{252}$ .

$\sqrt{- 1} \cdot \sqrt{252}$

Step 3

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

$i \cdot \sqrt{252}$

Step 4

Rewrite $252$ as $6^{2} \cdot 7$ .

Factor $36$ out of $252$ .

$i \cdot \sqrt{36 (7)}$

Rewrite $36$ as $6^{2}$ .

$i \cdot \sqrt{6^{2} \cdot 7}$

Step 5

Pull terms out from under the radical.

$i \cdot (6 \sqrt{7})$

Step 6

Move $6$ to the left of $i$ .

$6 i \sqrt{7}$