Simplify square root of -147

$\sqrt{- 147}$

Step 1

Rewrite $- 147$ as $- 1 (147)$ .

$\sqrt{- 1 (147)}$

Step 2

Rewrite $\sqrt{- 1 (147)}$ as $\sqrt{- 1} \cdot \sqrt{147}$ .

$\sqrt{- 1} \cdot \sqrt{147}$

Step 3

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

$i \cdot \sqrt{147}$

Step 4

Rewrite $147$ as $7^{2} \cdot 3$ .

Factor $49$ out of $147$ .

$i \cdot \sqrt{49 (3)}$

Rewrite $49$ as $7^{2}$ .

$i \cdot \sqrt{7^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$i \cdot (7 \sqrt{3})$

Step 6

Move $7$ to the left of $i$ .

$7 i \sqrt{3}$