Evaluate square root of -12

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Algebra

$\sqrt{- 12}$

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

$\sqrt{- 1 (12)}$

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

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

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

$i \cdot \sqrt{12}$

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

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Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

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

$2 i \sqrt{3}$

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