Basic Math Examples

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

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

Step 1

Rewrite the division as a fraction.

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

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

Step 2

Combine

\sqrt{2}

$\sqrt{2}$ and

\sqrt{8}

$\sqrt{8}$ into a single radical.

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

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

Step 3

Cancel the common factor of

2

$2$ and

8

$8$ .

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Step 3.1

Factor

2

$2$ out of

2

$2$ .

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

2

$2$ out of

8

$8$ .

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

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

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.

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

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

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

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.

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

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

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

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

$2$ .

$\frac{2}{3}$

$\frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$