Simplify 3+ square root of -16

$3 + \sqrt{- 16}$

Step 1

Rewrite $- 16$ as $- 1 (16)$ .

$3 + \sqrt{- 1 (16)}$

Step 2

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$3 + \sqrt{- 1} \cdot \sqrt{16}$

Step 3

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

$3 + i \cdot \sqrt{16}$

Step 4

Rewrite $16$ as $4^{2}$ .

$3 + i \cdot \sqrt{4^{2}}$

Step 5

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

$3 + i \cdot 4$

Step 6

Move $4$ to the left of $i$ .

$3 + 4 i$