Simplify ( square root of -32)/( square root of -50)

$\frac{\sqrt{- 32}}{\sqrt{- 50}}$

Pull out imaginary unit $i$ .

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

$\frac{\sqrt{- 1 (32)}}{\sqrt{- 50}}$

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

$\frac{\sqrt{- 1} \cdot \sqrt{32}}{\sqrt{- 50}}$

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

$\frac{i \cdot \sqrt{32}}{\sqrt{- 50}}$

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

$\frac{i \cdot \sqrt{32}}{\sqrt{- 1 (50)}}$

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

$\frac{i \cdot \sqrt{32}}{\sqrt{- 1} \cdot \sqrt{50}}$

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

$\frac{i \cdot \sqrt{32}}{i \cdot \sqrt{50}}$

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i \cdot \sqrt{32}}{i \cdot \sqrt{50}}$

Rewrite the expression.

$\frac{\sqrt{32}}{\sqrt{50}}$

Combine $\sqrt{32}$ and $\sqrt{50}$ into a single radical.

$\sqrt{\frac{32}{50}}$

Cancel the common factor of $32$ and $50$ .

Factor $2$ out of $32$ .

$\sqrt{\frac{2 (16)}{50}}$

Cancel the common factors.

Factor $2$ out of $50$ .

$\sqrt{\frac{2 \cdot 16}{2 \cdot 25}}$

Cancel the common factor.

$\sqrt{\frac{2 \cdot 16}{2 \cdot 25}}$

Rewrite the expression.

$\sqrt{\frac{16}{25}}$

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$\frac{\sqrt{16}}{\sqrt{25}}$

Simplify the numerator.

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

$\frac{\sqrt{4^{2}}}{\sqrt{25}}$

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

$\frac{4}{\sqrt{25}}$

Simplify the denominator.

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

$\frac{4}{\sqrt{5^{2}}}$

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

$\frac{4}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$

Simplify ( square root of -32)/( square root of -50)

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