Finite Math Examples

$\frac{\sqrt{- 48}}{\sqrt{- 75}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 48$ as $- 1 (48)$ .

$\frac{\sqrt{- 1 (48)}}{\sqrt{- 75}}$

Step 1.2

Rewrite $\sqrt{- 1 (48)}$ as $\sqrt{- 1} \cdot \sqrt{48}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{48}}{\sqrt{- 75}}$

Step 1.3

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

$\frac{i \cdot \sqrt{48}}{\sqrt{- 75}}$

Step 1.4

Rewrite $- 75$ as $- 1 (75)$ .

$\frac{i \cdot \sqrt{48}}{\sqrt{- 1 (75)}}$

Step 1.5

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$\frac{i \cdot \sqrt{48}}{\sqrt{- 1} \cdot \sqrt{75}}$

Step 1.6

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

$\frac{i \cdot \sqrt{48}}{i \cdot \sqrt{75}}$

Step 2

Cancel the common factor of $i$ .

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Step 2.1

Cancel the common factor.

$\frac{i \cdot \sqrt{48}}{i \cdot \sqrt{75}}$

Step 2.2

Rewrite the expression.

$\frac{\sqrt{48}}{\sqrt{75}}$

Step 3

Combine $\sqrt{48}$ and $\sqrt{75}$ into a single radical.

$\sqrt{\frac{48}{75}}$

Step 4

Cancel the common factor of $48$ and $75$ .

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Step 4.1

Factor $3$ out of $48$ .

$\sqrt{\frac{3 (16)}{75}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $75$ .

$\sqrt{\frac{3 \cdot 16}{3 \cdot 25}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{3 \cdot 16}{3 \cdot 25}}$

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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

Step 6

Simplify the numerator.

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Step 6.1

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

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

Step 6.2

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

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

Step 7

Simplify the denominator.

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Step 7.1

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

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

Step 7.2

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

$\frac{4}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$