Simplify - square root of 121+ square root of -1+ square root of 9+ square root of -25

$- \sqrt{121} + \sqrt{- 1} + \sqrt{9} + \sqrt{- 25}$

Simplify each term.

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

$- \sqrt{11^{2}} + \sqrt{- 1} + \sqrt{9} + \sqrt{- 25}$

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

$- 1 \cdot 11 + \sqrt{- 1} + \sqrt{9} + \sqrt{- 25}$

Multiply $- 1$ by $11$ .

$- 11 + \sqrt{- 1} + \sqrt{9} + \sqrt{- 25}$

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

$- 11 + i + \sqrt{9} + \sqrt{- 25}$

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

$- 11 + i + \sqrt{3^{2}} + \sqrt{- 25}$

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

$- 11 + i + 3 + \sqrt{- 25}$

Rewrite $- 25$ as $- 1 (25)$ .

$- 11 + i + 3 + \sqrt{- 1 (25)}$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$- 11 + i + 3 + \sqrt{- 1} \cdot \sqrt{25}$

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

$- 11 + i + 3 + i \cdot \sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$- 11 + i + 3 + i \cdot \sqrt{5^{2}}$

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

$- 11 + i + 3 + i \cdot 5$

Move $5$ to the left of $i$ .

$- 11 + i + 3 + 5 i$

Simplify by adding terms.

Add $- 11$ and $3$ .

$- 8 + i + 5 i$

Add $i$ and $5 i$ .

$- 8 + 6 i$