Simplify square root of -12*2i square root of -9

$\sqrt{- 12} \cdot 2 i \sqrt{- 9}$

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

$\sqrt{- 1 (12)} \cdot (2 i \sqrt{- 9})$

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

$\sqrt{- 1} \cdot \sqrt{12} \cdot (2 i \sqrt{- 9})$

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

$i \cdot \sqrt{12} \cdot (2 i \sqrt{- 9})$

Rewrite $- 9$ as $- 1 (9)$ .

$i \cdot \sqrt{12} \cdot (2 i \sqrt{- 1 (9)})$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$i \cdot \sqrt{12} \cdot (2 i (\sqrt{- 1} \cdot \sqrt{9}))$

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

$i \cdot \sqrt{12} \cdot (2 i (i \cdot \sqrt{9}))$

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

Factor $4$ out of $12$ .

$i \cdot \sqrt{4 (3)} \cdot (2 i (i \cdot \sqrt{9}))$

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

$i \cdot \sqrt{2^{2} \cdot 3} \cdot (2 i (i \cdot \sqrt{9}))$

Pull terms out from under the radical.

$i \cdot (2 \sqrt{3}) \cdot (2 i (i \cdot \sqrt{9}))$

Simplify the expression.

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

$2 \cdot i \sqrt{3} \cdot (2 i (i \cdot \sqrt{9}))$

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

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

Pull terms out from under the radical, assuming positive real numbers.

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

Move $3$ to the left of $i$ .

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

Multiply $2 i (3 i)$ .

Multiply $3$ by $2$ .

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

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

$2 i \sqrt{3} \cdot (6 (i^{1} i))$

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

$2 i \sqrt{3} \cdot (6 (i^{1} i^{1}))$

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

$2 i \sqrt{3} \cdot (6 i^{1 + 1})$

Add $1$ and $1$ .

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

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

$2 i \sqrt{3} \cdot (6 \cdot - 1)$

Multiply $6$ by $- 1$ .

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

Multiply $- 6$ by $2$ .

$- 12 i \sqrt{3}$

Simplify square root of -12*2i square root of -9

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