Simplify square root of -8* square root of 24

$\sqrt{- 8 \cdot \sqrt{24}}$

Step 1

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

Factor $4$ out of $24$ .

$\sqrt{- 8 \sqrt{4 (6)}}$

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

$\sqrt{- 8 \sqrt{2^{2} \cdot 6}}$

Step 2

Pull terms out from under the radical.

$\sqrt{- 8 \cdot 2 \sqrt{6}}$

Step 3

Multiply $- 8$ by $2$ .

$\sqrt{- 16 \sqrt{6}}$

Step 4

Rewrite $- 16 \sqrt{6}$ as ${(2^{2} i)}^{2} \sqrt{6}$ .

Rewrite $- 16$ as ${(4 i)}^{2}$ .

$\sqrt{{(4 i)}^{2} \sqrt{6}}$

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Raise $2$ to the power of $2$ .

$4 i \sqrt{\sqrt{6}}$

Step 7

Rewrite $\sqrt{\sqrt{6}}$ as $\sqrt[4]{6}$ .

$4 i \sqrt[4]{6}$