Simplify - square root of 100+ square root of -9+ square root of 9- square root of -16

$- \sqrt{100} + \sqrt{- 9} + \sqrt{9} - \sqrt{- 16}$

Simplify each term.

Rewrite $100$ as $10^{2}$ .

$- \sqrt{10^{2}} + \sqrt{- 9} + \sqrt{9} - \sqrt{- 16}$

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

$- 1 \cdot 10 + \sqrt{- 9} + \sqrt{9} - \sqrt{- 16}$

Multiply $- 1$ by $10$ .

$- 10 + \sqrt{- 9} + \sqrt{9} - \sqrt{- 16}$

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

$- 10 + \sqrt{- 1 (9)} + \sqrt{9} - \sqrt{- 16}$

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

$- 10 + \sqrt{- 1} \cdot \sqrt{9} + \sqrt{9} - \sqrt{- 16}$

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

$- 10 + i \cdot \sqrt{9} + \sqrt{9} - \sqrt{- 16}$

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

$- 10 + i \cdot \sqrt{3^{2}} + \sqrt{9} - \sqrt{- 16}$

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

$- 10 + i \cdot 3 + \sqrt{9} - \sqrt{- 16}$

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

$- 10 + 3 \cdot i + \sqrt{9} - \sqrt{- 16}$

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

$- 10 + 3 i + \sqrt{3^{2}} - \sqrt{- 16}$

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

$- 10 + 3 i + 3 - \sqrt{- 16}$

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

$- 10 + 3 i + 3 - \sqrt{- 1 (16)}$

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

$- 10 + 3 i + 3 - (\sqrt{- 1} \cdot \sqrt{16})$

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

$- 10 + 3 i + 3 - (i \cdot \sqrt{16})$

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

$- 10 + 3 i + 3 - (i \cdot \sqrt{4^{2}})$

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

$- 10 + 3 i + 3 - (i \cdot 4)$

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

$- 10 + 3 i + 3 - (4 \cdot i)$

Multiply $4$ by $- 1$ .

$- 10 + 3 i + 3 - 4 i$

Simplify by adding terms.

Add $- 10$ and $3$ .

$- 7 + 3 i - 4 i$

Subtract $4 i$ from $3 i$ .

$- 7 - i$