Evaluate square root of -50

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Algebra

$\sqrt{- 50}$

Rewrite $- 50$ as $- 1 (50)$ .

$\sqrt{- 1 (50)}$

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$\sqrt{- 1} \cdot \sqrt{50}$

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

$i \cdot \sqrt{50}$

Rewrite $50$ as $5^{2} \cdot 2$ .

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Factor $25$ out of $50$ .

$i \cdot \sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

$i \cdot \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$i \cdot (5 \sqrt{2})$

Move $5$ to the left of $i$ .

$5 i \sqrt{2}$

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