Evaluate square root of -48

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Algebra

$\sqrt{- 48}$

Rewrite $- 48$ as $- 1 (48)$ .

$\sqrt{- 1 (48)}$

Rewrite $\sqrt{- 1 (48)}$ as $\sqrt{- 1} \cdot \sqrt{48}$ .

$\sqrt{- 1} \cdot \sqrt{48}$

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

$i \cdot \sqrt{48}$

Rewrite $48$ as $4^{2} \cdot 3$ .

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Factor $16$ out of $48$ .

$i \cdot \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

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

Pull terms out from under the radical.

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

Move $4$ to the left of $i$ .

$4 i \sqrt{3}$

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