Basic Math Examples

$4 \sqrt{2} \div 3 \sqrt{8}$

Step 1

Rewrite the division as a fraction.

$\frac{4 \sqrt{2}}{3 \sqrt{8}}$

Step 2

Combine $\sqrt{2}$ and $\sqrt{8}$ into a single radical.

$\frac{4 \sqrt{\frac{2}{8}}}{3}$

Step 3

Cancel the common factor of $2$ and $8$ .

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Step 3.1

Factor $2$ out of $2$ .

$\frac{4 \sqrt{\frac{2 (1)}{8}}}{3}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $8$ .

$\frac{4 \sqrt{\frac{2 \cdot 1}{2 \cdot 4}}}{3}$

Step 3.2.2

Cancel the common factor.

$\frac{4 \sqrt{\frac{2 \cdot 1}{2 \cdot 4}}}{3}$

Step 3.2.3

Rewrite the expression.

$\frac{4 \sqrt{\frac{1}{4}}}{3}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$\frac{4 \frac{\sqrt{1}}{\sqrt{4}}}{3}$

Step 4.2

Any root of $1$ is $1$ .

$\frac{4 \frac{1}{\sqrt{4}}}{3}$

Step 4.3

Simplify the denominator.

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Step 4.3.1

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

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

Step 4.3.2

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

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

Step 5

Combine fractions.

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Step 5.1

Combine $4$ and $\frac{1}{2}$ .

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

Step 5.2

Divide $4$ by $2$ .

$\frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$