Simplify -2i square root of -12

$- 2 i \sqrt{- 12}$

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

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

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

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

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

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

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

Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

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

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

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

Multiply $2$ by $- 2$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

$- 4 \cdot - 1 \sqrt{3}$

Multiply $- 4$ by $- 1$ .

$4 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{3}$

Decimal Form:

$6.92820323 \dots$