Simplify 5+ square root of -64

$5 + \sqrt{- 64}$

Step 1

Rewrite $- 64$ as $- 1 (64)$ .

$5 + \sqrt{- 1 (64)}$

Step 2

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$5 + \sqrt{- 1} \cdot \sqrt{64}$

Step 3

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

$5 + i \cdot \sqrt{64}$

Step 4

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

$5 + i \cdot \sqrt{8^{2}}$

Step 5

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

$5 + i \cdot 8$

Step 6

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

$5 + 8 i$