Simplify square root of -24* square root of 3

$\sqrt{- 24} \cdot \sqrt{3}$

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

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

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

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

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

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

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

Factor $4$ out of $24$ .

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

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

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

Pull terms out from under the radical.

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

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

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

Multiply $2 i \sqrt{6} \sqrt{3}$ .

Combine using the product rule for radicals.

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

Multiply $3$ by $6$ .

$2 i \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$2 i \sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

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

Pull terms out from under the radical.

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

Multiply $3$ by $2$ .

$6 i \sqrt{2}$