Simplify the Radical Expression - square root of 64- square root of -50+ square root of 36- square root of -32

$- \sqrt{64} - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Simplify each term.

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

$- \sqrt{8^{2}} - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Pull terms out from under the radical.

$- | 8 | - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

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

$- 1 \cdot 8 - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Multiply $- 1$ by $8$ .

$- 8 - \sqrt{- 50} + \sqrt{36} - \sqrt{- 32}$

Rewrite $- 50$ as $- 1 (50)$ .

$- 8 - \sqrt{- 1 (50)} + \sqrt{36} - \sqrt{- 32}$

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$- 8 - (\sqrt{- 1} \cdot \sqrt{50}) + \sqrt{36} - \sqrt{- 32}$

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

$- 8 - (i \cdot \sqrt{50}) + \sqrt{36} - \sqrt{- 32}$

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$- 8 - (i \cdot \sqrt{25 (2)}) + \sqrt{36} - \sqrt{- 32}$

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

$- 8 - (i \cdot \sqrt{5^{2} \cdot 2}) + \sqrt{36} - \sqrt{- 32}$

Pull terms out from under the radical.

$- 8 - (i \cdot (| 5 | \sqrt{2})) + \sqrt{36} - \sqrt{- 32}$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$- 8 - (i \cdot (5 \sqrt{2})) + \sqrt{36} - \sqrt{- 32}$

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

$- 8 - (5 \cdot i \sqrt{2}) + \sqrt{36} - \sqrt{- 32}$

Multiply $5$ by $- 1$ .

$- 8 - 5 (i \sqrt{2}) + \sqrt{36} - \sqrt{- 32}$

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

$- 8 - 5 i \sqrt{2} + \sqrt{6^{2}} - \sqrt{- 32}$

Pull terms out from under the radical.

$- 8 - 5 i \sqrt{2} + | 6 | - \sqrt{- 32}$

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

$- 8 - 5 i \sqrt{2} + 6 - \sqrt{- 32}$

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

$- 8 - 5 i \sqrt{2} + 6 - \sqrt{- 1 (32)}$

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

$- 8 - 5 i \sqrt{2} + 6 - (\sqrt{- 1} \cdot \sqrt{32})$

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

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot \sqrt{32})$

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

Factor $16$ out of $32$ .

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot \sqrt{16 (2)})$

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

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot \sqrt{4^{2} \cdot 2})$

Pull terms out from under the radical.

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot (| 4 | \sqrt{2}))$

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

$- 8 - 5 i \sqrt{2} + 6 - (i \cdot (4 \sqrt{2}))$

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

$- 8 - 5 i \sqrt{2} + 6 - (4 \cdot i \sqrt{2})$

Multiply $4$ by $- 1$ .

$- 8 - 5 i \sqrt{2} + 6 - 4 i \sqrt{2}$

Add $- 8$ and $6$ .

$- 5 i \sqrt{2} - 2 - 4 i \sqrt{2}$

Subtract $4 i \sqrt{2}$ from $- 5 i \sqrt{2}$ .

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

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

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

Simplify the Radical Expression - square root of 64- square root of -50+ square root of 36- square root of -32

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