Simplify square root of -8* square root of -12

$\sqrt{- 8} \cdot \sqrt{- 12}$

Rewrite $- 8$ as $- 1 (8)$ .

$\sqrt{- 1 (8)} \cdot \sqrt{- 12}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$\sqrt{- 1} \cdot \sqrt{8} \cdot \sqrt{- 12}$

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

$i \cdot \sqrt{8} \cdot \sqrt{- 12}$

Rewrite $- 12$ as $- 1 (12)$ .

$i \cdot \sqrt{8} \cdot \sqrt{- 1 (12)}$

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$i \cdot \sqrt{8} \cdot (\sqrt{- 1} \cdot \sqrt{12})$

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

$i \cdot \sqrt{8} \cdot (i \cdot \sqrt{12})$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$i \cdot \sqrt{4 (2)} \cdot (i \cdot \sqrt{12})$

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

$i \cdot \sqrt{2^{2} \cdot 2} \cdot (i \cdot \sqrt{12})$

Pull terms out from under the radical.

$i \cdot (2 \sqrt{2}) \cdot (i \cdot \sqrt{12})$

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

$2 \cdot i \sqrt{2} \cdot (i \cdot \sqrt{12})$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$2 i \sqrt{2} \cdot (i \cdot \sqrt{4 (3)})$

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

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

Pull terms out from under the radical.

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

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

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

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

Multiply $2$ by $2$ .

$4 i \sqrt{2} (i \sqrt{3})$

Raise $i$ to the power of $1$ .

$4 (i^{1} i) \sqrt{2} \sqrt{3}$

Raise $i$ to the power of $1$ .

$4 (i^{1} i^{1}) \sqrt{2} \sqrt{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 i^{1 + 1} \sqrt{2} \sqrt{3}$

Add $1$ and $1$ .

$4 i^{2} \sqrt{2} \sqrt{3}$

Combine using the product rule for radicals.

$4 i^{2} \sqrt{3 \cdot 2}$

Multiply $3$ by $2$ .

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

Rewrite $i^{2}$ as $- 1$ .

$4 \cdot - 1 \sqrt{6}$

Multiply $4$ by $- 1$ .

$- 4 \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$- 4 \sqrt{6}$

Decimal Form:

$- 9.79795897 \dots$

Simplify square root of -8* square root of -12

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