Simplify - square root of 1- square root of -100- square root of 121+ square root of -1

$- \sqrt{1} - \sqrt{- 100} - \sqrt{121} + \sqrt{- 1}$

Simplify each term.

Any root of $1$ is $1$ .

$- 1 \cdot 1 - \sqrt{- 100} - \sqrt{121} + \sqrt{- 1}$

Multiply $- 1$ by $1$ .

$- 1 - \sqrt{- 100} - \sqrt{121} + \sqrt{- 1}$

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

$- 1 - \sqrt{- 1 (100)} - \sqrt{121} + \sqrt{- 1}$

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

$- 1 - (\sqrt{- 1} \cdot \sqrt{100}) - \sqrt{121} + \sqrt{- 1}$

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

$- 1 - (i \cdot \sqrt{100}) - \sqrt{121} + \sqrt{- 1}$

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

$- 1 - (i \cdot \sqrt{10^{2}}) - \sqrt{121} + \sqrt{- 1}$

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

$- 1 - (i \cdot 10) - \sqrt{121} + \sqrt{- 1}$

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

$- 1 - (10 \cdot i) - \sqrt{121} + \sqrt{- 1}$

Multiply $10$ by $- 1$ .

$- 1 - 10 i - \sqrt{121} + \sqrt{- 1}$

Rewrite $121$ as $11^{2}$ .

$- 1 - 10 i - \sqrt{11^{2}} + \sqrt{- 1}$

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

$- 1 - 10 i - 1 \cdot 11 + \sqrt{- 1}$

Multiply $- 1$ by $11$ .

$- 1 - 10 i - 11 + \sqrt{- 1}$

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

$- 1 - 10 i - 11 + i$

Simplify by adding terms.

Subtract $11$ from $- 1$ .

$- 12 - 10 i + i$

Add $- 10 i$ and $i$ .

$- 12 - 9 i$