Simplify square root of -300

$\sqrt{- 300}$

Rewrite $- 300$ as $- 1 (300)$ .

$\sqrt{- 1 (300)}$

Rewrite $\sqrt{- 1 (300)}$ as $\sqrt{- 1} \cdot \sqrt{300}$ .

$\sqrt{- 1} \cdot \sqrt{300}$

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

$i \cdot \sqrt{300}$

Rewrite $300$ as $10^{2} \cdot 3$ .

Factor $100$ out of $300$ .

$i \cdot \sqrt{100 (3)}$

Rewrite $100$ as $10^{2}$ .

$i \cdot \sqrt{10^{2} \cdot 3}$

Pull terms out from under the radical.

$i \cdot (10 \sqrt{3})$

Move $10$ to the left of $i$ .

$10 i \sqrt{3}$