Simplify 3 square root of -24

$3 \sqrt{- 24}$

Step 1

Rewrite $- 24$ as $- 1 (24)$ .

$3 \sqrt{- 1 (24)}$

Step 2

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$3 (\sqrt{- 1} \cdot \sqrt{24})$

Step 3

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

$3 (i \cdot \sqrt{24})$

Step 4

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$3 (i \cdot \sqrt{4 (6)})$

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

$3 (i \cdot \sqrt{2^{2} \cdot 6})$

Step 5

Pull terms out from under the radical.

$3 (i \cdot (2 \sqrt{6}))$

Step 6

Simplify the expression.

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

$3 (2 \cdot i \sqrt{6})$

Multiply $2$ by $3$ .

$6 i \sqrt{6}$