Simplify 3 square root of 16+ square root of -9

$3 \sqrt{16} + \sqrt{- 9}$

Step 1

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

$3 \sqrt{4^{2}} + \sqrt{- 9}$

Step 2

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

$3 \cdot 4 + \sqrt{- 9}$

Step 3

Multiply $3$ by $4$ .

$12 + \sqrt{- 9}$

Step 4

Rewrite $- 9$ as $- 1 (9)$ .

$12 + \sqrt{- 1 (9)}$

Step 5

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$12 + \sqrt{- 1} \cdot \sqrt{9}$

Step 6

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

$12 + i \cdot \sqrt{9}$

Step 7

Rewrite $9$ as $3^{2}$ .

$12 + i \cdot \sqrt{3^{2}}$

Step 8

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

$12 + i \cdot 3$

Step 9

Move $3$ to the left of $i$ .

$12 + 3 i$