Simplify square root of 4+ square root of -100- square root of 9- square root of -81

$\sqrt{4} + \sqrt{- 100} - \sqrt{9} - \sqrt{- 81}$

Simplify each term.

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

$\sqrt{2^{2}} + \sqrt{- 100} - \sqrt{9} - \sqrt{- 81}$

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

$2 + \sqrt{- 100} - \sqrt{9} - \sqrt{- 81}$

Rewrite $- 100$ as $- 1 (100)$ .

$2 + \sqrt{- 1 (100)} - \sqrt{9} - \sqrt{- 81}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$2 + \sqrt{- 1} \cdot \sqrt{100} - \sqrt{9} - \sqrt{- 81}$

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

$2 + i \cdot \sqrt{100} - \sqrt{9} - \sqrt{- 81}$

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

$2 + i \cdot \sqrt{10^{2}} - \sqrt{9} - \sqrt{- 81}$

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

$2 + i \cdot 10 - \sqrt{9} - \sqrt{- 81}$

Move $10$ to the left of $i$ .

$2 + 10 \cdot i - \sqrt{9} - \sqrt{- 81}$

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

$2 + 10 i - \sqrt{3^{2}} - \sqrt{- 81}$

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

$2 + 10 i - 1 \cdot 3 - \sqrt{- 81}$

Multiply $- 1$ by $3$ .

$2 + 10 i - 3 - \sqrt{- 81}$

Rewrite $- 81$ as $- 1 (81)$ .

$2 + 10 i - 3 - \sqrt{- 1 (81)}$

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$2 + 10 i - 3 - (\sqrt{- 1} \cdot \sqrt{81})$

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

$2 + 10 i - 3 - (i \cdot \sqrt{81})$

Rewrite $81$ as $9^{2}$ .

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

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

$2 + 10 i - 3 - (i \cdot 9)$

Move $9$ to the left of $i$ .

$2 + 10 i - 3 - (9 \cdot i)$

Multiply $9$ by $- 1$ .

$2 + 10 i - 3 - 9 i$

Simplify by adding terms.

Subtract $3$ from $2$ .

$- 1 + 10 i - 9 i$

Subtract $9 i$ from $10 i$ .

$- 1 + i$