Basic Math Examples

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

Step 1

Combine $\sqrt{2}$ and $\sqrt{18}$ into a single radical.

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

Step 2

Cancel the common factor of $2$ and $18$ .

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Step 2.1

Factor $2$ out of $2$ .

$\frac{5 \sqrt{\frac{2 (1)}{18}}}{4}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $18$ .

$\frac{5 \sqrt{\frac{2 \cdot 1}{2 \cdot 9}}}{4}$

Step 2.2.2

Cancel the common factor.

$\frac{5 \sqrt{\frac{2 \cdot 1}{2 \cdot 9}}}{4}$

Step 2.2.3

Rewrite the expression.

$\frac{5 \sqrt{\frac{1}{9}}}{4}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $\sqrt{\frac{1}{9}}$ as $\frac{\sqrt{1}}{\sqrt{9}}$ .

$\frac{5 \frac{\sqrt{1}}{\sqrt{9}}}{4}$

Step 3.2

Any root of $1$ is $1$ .

$\frac{5 \frac{1}{\sqrt{9}}}{4}$

Step 3.3

Simplify the denominator.

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Step 3.3.1

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

$\frac{5 \frac{1}{\sqrt{3^{2}}}}{4}$

Step 3.3.2

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

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

Step 4

Combine $5$ and $\frac{1}{3}$ .

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

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{3} \cdot \frac{1}{4}$

Step 6

Multiply $\frac{5}{3} \cdot \frac{1}{4}$ .

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Step 6.1

Multiply $\frac{5}{3}$ by $\frac{1}{4}$ .

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

Step 6.2

Multiply $3$ by $4$ .

$\frac{5}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{12}$

Decimal Form:

$0.41\overline{6}$