Simplify square root of -52

$\sqrt{- 52}$

Step 1

Rewrite $- 52$ as $- 1 (52)$ .

$\sqrt{- 1 (52)}$

Step 2

Rewrite $\sqrt{- 1 (52)}$ as $\sqrt{- 1} \cdot \sqrt{52}$ .

$\sqrt{- 1} \cdot \sqrt{52}$

Step 3

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

$i \cdot \sqrt{52}$

Step 4

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$i \cdot \sqrt{4 (13)}$

Rewrite $4$ as $2^{2}$ .

$i \cdot \sqrt{2^{2} \cdot 13}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{13})$

Step 6

Move $2$ to the left of $i$ .

$2 i \sqrt{13}$