Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Factor $2$ out of $8$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $18$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Simplify the numerator.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Simplify the denominator.

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Multiply $5 (\frac{2}{3})$ .

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Step 6.1

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

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

Step 6.2

Multiply $5$ by $2$ .

$\frac{10}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{3}$

Decimal Form:

$3.\overline{3}$

Mixed Number Form:

$3 \frac{1}{3}$