Simplify square root of -128

$\sqrt{- 128}$

Step 1

Rewrite $- 128$ as $- 1 (128)$ .

$\sqrt{- 1 (128)}$

Step 2

Rewrite $\sqrt{- 1 (128)}$ as $\sqrt{- 1} \cdot \sqrt{128}$ .

$\sqrt{- 1} \cdot \sqrt{128}$

Step 3

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

$i \cdot \sqrt{128}$

Step 4

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$i \cdot \sqrt{64 (2)}$

Rewrite $64$ as $8^{2}$ .

$i \cdot \sqrt{8^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$i \cdot (8 \sqrt{2})$

Step 6

Move $8$ to the left of $i$ .

$8 i \sqrt{2}$