Simplify square root of -16+ square root of 49

$\sqrt{- 16} + \sqrt{49}$

Step 1

Simplify each term.

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

$\sqrt{- 1 (16)} + \sqrt{49}$

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

$\sqrt{- 1} \cdot \sqrt{16} + \sqrt{49}$

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

$i \cdot \sqrt{16} + \sqrt{49}$

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

$i \cdot \sqrt{4^{2}} + \sqrt{49}$

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

$i \cdot 4 + \sqrt{49}$

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

$4 \cdot i + \sqrt{49}$

Rewrite $49$ as $7^{2}$ .

$4 i + \sqrt{7^{2}}$

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

$4 i + 7$

Step 2

Reorder $4 i$ and $7$ .

$7 + 4 i$