Simplify square root of -200

$\sqrt{- 200}$

Step 1

Rewrite $- 200$ as $- 1 (200)$ .

$\sqrt{- 1 (200)}$

Step 2

Rewrite $\sqrt{- 1 (200)}$ as $\sqrt{- 1} \cdot \sqrt{200}$ .

$\sqrt{- 1} \cdot \sqrt{200}$

Step 3

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

$i \cdot \sqrt{200}$

Step 4

Rewrite $200$ as $10^{2} \cdot 2$ .

Factor $100$ out of $200$ .

$i \cdot \sqrt{100 (2)}$

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

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

Step 5

Pull terms out from under the radical.

$i \cdot (10 \sqrt{2})$

Step 6

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

$10 i \sqrt{2}$