Simplify the Radical Expression - 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.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

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

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.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

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

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.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

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

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.

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

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

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

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

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

Add $- 6$ and $4$ .

$- 2 + 6 i + 3 i$

Add $6 i$ and $3 i$ .

$- 2 + 9 i$

Simplify the Radical Expression - square root of 36+ square root of -36+ square root of 16+ square root of -9

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