Simplify 3 square root of -12*2 square root of -2

$3 \sqrt{- 12} \cdot 2 \sqrt{- 2}$

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

$3 \sqrt{- 1 (12)} \cdot (2 \sqrt{- 2})$

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

$3 (\sqrt{- 1} \cdot \sqrt{12}) \cdot (2 \sqrt{- 2})$

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

$3 (i \cdot \sqrt{12}) \cdot (2 \sqrt{- 2})$

Rewrite $- 2$ as $- 1 (2)$ .

$3 (i \cdot \sqrt{12}) \cdot (2 \sqrt{- 1 (2)})$

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$3 (i \cdot \sqrt{12}) \cdot (2 (\sqrt{- 1} \cdot \sqrt{2}))$

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

$3 (i \cdot \sqrt{12}) \cdot (2 (i \cdot \sqrt{2}))$

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

Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

Simplify the expression.

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

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

Multiply $2$ by $3$ .

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

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

Multiply $2$ by $6$ .

$12 i \sqrt{3} (i \sqrt{2})$

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

$12 (i^{1} i) \sqrt{3} \sqrt{2}$

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

$12 (i^{1} i^{1}) \sqrt{3} \sqrt{2}$

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

$12 i^{1 + 1} \sqrt{3} \sqrt{2}$

Add $1$ and $1$ .

$12 i^{2} \sqrt{3} \sqrt{2}$

Combine using the product rule for radicals.

$12 i^{2} \sqrt{2 \cdot 3}$

Multiply $2$ by $3$ .

$12 i^{2} \sqrt{6}$

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

$12 \cdot - 1 \sqrt{6}$

Multiply $12$ by $- 1$ .

$- 12 \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$- 12 \sqrt{6}$

Decimal Form:

$- 29.39387691 \dots$

Simplify 3 square root of -12*2 square root of -2

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