Evaluate square root of -400

$\sqrt{- 400}$

Step 1

Rewrite $- 400$ as $- 1 (400)$ .

$\sqrt{- 1 (400)}$

Step 2

Rewrite $\sqrt{- 1 (400)}$ as $\sqrt{- 1} \cdot \sqrt{400}$ .

$\sqrt{- 1} \cdot \sqrt{400}$

Step 3

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

$i \cdot \sqrt{400}$

Step 4

Rewrite $400$ as $20^{2}$ .

$i \cdot \sqrt{20^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 20$

Step 6

Move $20$ to the left of $i$ .

$20 i$