Evaluate ( square root of -64)/( square root of -2)

$\frac{\sqrt{- 64}}{\sqrt{- 2}}$

Pull out imaginary unit $i$ .

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Rewrite $- 64$ as $- 1 (64)$ .

$\frac{\sqrt{- 1 (64)}}{\sqrt{- 2}}$

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{64}}{\sqrt{- 2}}$

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

$\frac{i \cdot \sqrt{64}}{\sqrt{- 2}}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{i \cdot \sqrt{64}}{\sqrt{- 1 (2)}}$

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$\frac{i \cdot \sqrt{64}}{\sqrt{- 1} \cdot \sqrt{2}}$

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

$\frac{i \cdot \sqrt{64}}{i \cdot \sqrt{2}}$

Cancel the common factor of $i$ .

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Cancel the common factor.

$\frac{i \cdot \sqrt{64}}{i \cdot \sqrt{2}}$

Rewrite the expression.

$\frac{\sqrt{64}}{\sqrt{2}}$

Combine $\sqrt{64}$ and $\sqrt{2}$ into a single radical.

$\sqrt{\frac{64}{2}}$

Divide $64$ by $2$ .

$\sqrt{32}$

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

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Factor $16$ out of $32$ .

$\sqrt{16 (2)}$

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

$\sqrt{4^{2} \cdot 2}$

Pull terms out from under the radical.

$4 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{2}$

Decimal Form:

$5.65685424 \dots$

Evaluate ( square root of -64)/( square root of -2)

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