Simplify the Radical Expression square root of -252

$\sqrt{- 252}$

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

$\sqrt{- 1 (252)}$

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

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

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

$i \cdot \sqrt{252}$

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

Factor $36$ out of $252$ .

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

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

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

Pull terms out from under the radical.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

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

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

$6 i \sqrt{7}$