Simplify - square root of 36+ square root of -36+ square root of 16+ square root of -9

$- \sqrt{36} + \sqrt{- 36} + \sqrt{16} + \sqrt{- 9}$

Simplify each term.

Rewrite $36$ as $6^{2}$ .

$- \sqrt{6^{2}} + \sqrt{- 36} + \sqrt{16} + \sqrt{- 9}$

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

$- 1 \cdot 6 + \sqrt{- 36} + \sqrt{16} + \sqrt{- 9}$

Multiply $- 1$ by $6$ .

$- 6 + \sqrt{- 36} + \sqrt{16} + \sqrt{- 9}$

Rewrite $- 36$ as $- 1 (36)$ .

$- 6 + \sqrt{- 1 (36)} + \sqrt{16} + \sqrt{- 9}$

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$- 6 + \sqrt{- 1} \cdot \sqrt{36} + \sqrt{16} + \sqrt{- 9}$

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

$- 6 + i \cdot \sqrt{36} + \sqrt{16} + \sqrt{- 9}$

Rewrite $36$ as $6^{2}$ .

$- 6 + i \cdot \sqrt{6^{2}} + \sqrt{16} + \sqrt{- 9}$

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

$- 6 + i \cdot 6 + \sqrt{16} + \sqrt{- 9}$

Move $6$ to the left of $i$ .

$- 6 + 6 \cdot i + \sqrt{16} + \sqrt{- 9}$

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

$- 6 + 6 i + \sqrt{4^{2}} + \sqrt{- 9}$

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

$- 6 + 6 i + 4 + \sqrt{- 9}$

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

$- 6 + 6 i + 4 + \sqrt{- 1 (9)}$

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

$- 6 + 6 i + 4 + \sqrt{- 1} \cdot \sqrt{9}$

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

$- 6 + 6 i + 4 + i \cdot \sqrt{9}$

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

$- 6 + 6 i + 4 + i \cdot \sqrt{3^{2}}$

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

$- 6 + 6 i + 4 + i \cdot 3$

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

$- 6 + 6 i + 4 + 3 i$

Simplify by adding terms.

Add $- 6$ and $4$ .

$- 2 + 6 i + 3 i$

Add $6 i$ and $3 i$ .

$- 2 + 9 i$