Simplify square root of -256

$\sqrt{- 256}$

Step 1

Rewrite $- 256$ as $- 1 (256)$ .

$\sqrt{- 1 (256)}$

Step 2

Rewrite $\sqrt{- 1 (256)}$ as $\sqrt{- 1} \cdot \sqrt{256}$ .

$\sqrt{- 1} \cdot \sqrt{256}$

Step 3

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

$i \cdot \sqrt{256}$

Step 4

Rewrite $256$ as $16^{2}$ .

$i \cdot \sqrt{16^{2}}$

Step 5

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

$i \cdot 16$

Step 6

Move $16$ to the left of $i$ .

$16 i$