Simplify square root of (-7)^3

$\sqrt{{(- 7)}^{3}}$

Step 1

Raise $- 7$ to the power of $3$ .

$\sqrt{- 343}$

Step 2

Rewrite $- 343$ as $- 1 (343)$ .

$\sqrt{- 1 (343)}$

Step 3

Rewrite $\sqrt{- 1 (343)}$ as $\sqrt{- 1} \cdot \sqrt{343}$ .

$\sqrt{- 1} \cdot \sqrt{343}$

Step 4

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

$i \cdot \sqrt{343}$

Step 5

Rewrite $343$ as $7^{2} \cdot 7$ .

Factor $49$ out of $343$ .

$i \cdot \sqrt{49 (7)}$

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

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

$7 i \sqrt{7}$