Algebra Examples

$\frac{5 \sqrt{8}}{4 \sqrt{18}}$

Step 1

Combine $\sqrt{8}$ and $\sqrt{18}$ into a single radical.

$\frac{5 \sqrt{\frac{8}{18}}}{4}$

Step 2

Cancel the common factor of $8$ and $18$ .

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Step 2.1

Factor $2$ out of $8$ .

$\frac{5 \sqrt{\frac{2 (4)}{18}}}{4}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $18$ .

$\frac{5 \sqrt{\frac{2 \cdot 4}{2 \cdot 9}}}{4}$

Step 2.2.2

Cancel the common factor.

$\frac{5 \sqrt{\frac{2 \cdot 4}{2 \cdot 9}}}{4}$

Step 2.2.3

Rewrite the expression.

$\frac{5 \sqrt{\frac{4}{9}}}{4}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $\sqrt{\frac{4}{9}}$ as $\frac{\sqrt{4}}{\sqrt{9}}$ .

$\frac{5 \frac{\sqrt{4}}{\sqrt{9}}}{4}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

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

$\frac{5 \frac{\sqrt{2^{2}}}{\sqrt{9}}}{4}$

Step 3.2.2

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

$\frac{5 \frac{2}{\sqrt{9}}}{4}$

Step 3.3

Simplify the denominator.

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Step 3.3.1

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

$\frac{5 \frac{2}{\sqrt{3^{2}}}}{4}$

Step 3.3.2

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

$\frac{5 (\frac{2}{3})}{4}$

Step 4

Combine fractions.

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Step 4.1

Combine $5$ and $\frac{2}{3}$ .

$\frac{\frac{5 \cdot 2}{3}}{4}$

Step 4.2

Multiply $5$ by $2$ .

$\frac{\frac{10}{3}}{4}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{10}{3} \cdot \frac{1}{4}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{3} \cdot \frac{1}{4}$

Step 6.2

Factor $2$ out of $4$ .

$\frac{2 \cdot 5}{3} \cdot \frac{1}{2 \cdot 2}$

Step 6.3

Cancel the common factor.

$\frac{2 \cdot 5}{3} \cdot \frac{1}{2 \cdot 2}$

Step 6.4

Rewrite the expression.

$\frac{5}{3} \cdot \frac{1}{2}$

Step 7

Multiply $\frac{5}{3}$ by $\frac{1}{2}$ .

$\frac{5}{3 \cdot 2}$

Step 8

Multiply $3$ by $2$ .

$\frac{5}{6}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{6}$

Decimal Form:

$0.8\overline{3}$