Simplify the Radical Expression square root of 9- square root of -128+ square root of 36- square root of -32

$\sqrt{9} - \sqrt{- 128} + \sqrt{36} - \sqrt{- 32}$

Simplify each term.

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

$\sqrt{3^{2}} - \sqrt{- 128} + \sqrt{36} - \sqrt{- 32}$

Pull terms out from under the radical.

$| 3 | - \sqrt{- 128} + \sqrt{36} - \sqrt{- 32}$

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

$3 - \sqrt{- 128} + \sqrt{36} - \sqrt{- 32}$

Rewrite $- 128$ as $- 1 (128)$ .

$3 - \sqrt{- 1 (128)} + \sqrt{36} - \sqrt{- 32}$

Rewrite $\sqrt{- 1 (128)}$ as $\sqrt{- 1} \cdot \sqrt{128}$ .

$3 - (\sqrt{- 1} \cdot \sqrt{128}) + \sqrt{36} - \sqrt{- 32}$

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

$3 - (i \cdot \sqrt{128}) + \sqrt{36} - \sqrt{- 32}$

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$3 - (i \cdot \sqrt{64 (2)}) + \sqrt{36} - \sqrt{- 32}$

Rewrite $64$ as $8^{2}$ .

$3 - (i \cdot \sqrt{8^{2} \cdot 2}) + \sqrt{36} - \sqrt{- 32}$

Pull terms out from under the radical.

$3 - (i \cdot (| 8 | \sqrt{2})) + \sqrt{36} - \sqrt{- 32}$

The absolute value is the distance between a number and zero. The distance between $0$ and $8$ is $8$ .

$3 - (i \cdot (8 \sqrt{2})) + \sqrt{36} - \sqrt{- 32}$

Move $8$ to the left of $i$ .

$3 - (8 \cdot i \sqrt{2}) + \sqrt{36} - \sqrt{- 32}$

Multiply $8$ by $- 1$ .

$3 - 8 (i \sqrt{2}) + \sqrt{36} - \sqrt{- 32}$

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

$3 - 8 i \sqrt{2} + \sqrt{6^{2}} - \sqrt{- 32}$

Pull terms out from under the radical.

$3 - 8 i \sqrt{2} + | 6 | - \sqrt{- 32}$

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

$3 - 8 i \sqrt{2} + 6 - \sqrt{- 32}$

Rewrite $- 32$ as $- 1 (32)$ .

$3 - 8 i \sqrt{2} + 6 - \sqrt{- 1 (32)}$

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$3 - 8 i \sqrt{2} + 6 - (\sqrt{- 1} \cdot \sqrt{32})$

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

$3 - 8 i \sqrt{2} + 6 - (i \cdot \sqrt{32})$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$3 - 8 i \sqrt{2} + 6 - (i \cdot \sqrt{16 (2)})$

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

$3 - 8 i \sqrt{2} + 6 - (i \cdot \sqrt{4^{2} \cdot 2})$

Pull terms out from under the radical.

$3 - 8 i \sqrt{2} + 6 - (i \cdot (| 4 | \sqrt{2}))$

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

$3 - 8 i \sqrt{2} + 6 - (i \cdot (4 \sqrt{2}))$

Move $4$ to the left of $i$ .

$3 - 8 i \sqrt{2} + 6 - (4 \cdot i \sqrt{2})$

Multiply $4$ by $- 1$ .

$3 - 8 i \sqrt{2} + 6 - 4 i \sqrt{2}$

Add $3$ and $6$ .

$- 8 i \sqrt{2} + 9 - 4 i \sqrt{2}$

Subtract $4 i \sqrt{2}$ from $- 8 i \sqrt{2}$ .

$- 12 i \sqrt{2} + 9$

Reorder $- 12 i \sqrt{2}$ and $9$ .

$9 - 12 i \sqrt{2}$

Simplify the Radical Expression square root of 9- square root of -128+ square root of 36- square root of -32

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