Basic Math Examples

\frac{\sqrt{72}}{3}

$\frac{\sqrt{72}}{3}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite

72

$72$ as

6^{2} \cdot 2

$6^{2} \cdot 2$ .

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Step 1.1.1

Factor

36

$36$ out of

72

$72$ .

\frac{\sqrt{36 (2)}}{3}

$\frac{\sqrt{36 (2)}}{3}$

Step 1.1.2

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

\frac{\sqrt{6^{2} \cdot 2}}{3}

$\frac{\sqrt{6^{2} \cdot 2}}{3}$

\frac{\sqrt{6^{2} \cdot 2}}{3}

$\frac{\sqrt{6^{2} \cdot 2}}{3}$

Step 1.2

Pull terms out from under the radical.

\frac{6 \sqrt{2}}{3}

$\frac{6 \sqrt{2}}{3}$

\frac{6 \sqrt{2}}{3}

$\frac{6 \sqrt{2}}{3}$

Step 2

Cancel the common factor of

6

$6$ and

3

$3$ .

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Step 2.1

Factor

3

$3$ out of

6 \sqrt{2}

$6 \sqrt{2}$ .

\frac{3 (2 \sqrt{2})}{3}

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

3

$3$ out of

3

$3$ .

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

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

Step 2.2.2

Cancel the common factor.

$\frac{3 (2 \sqrt{2})}{3 \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{2 \sqrt{2}}{1}$

Step 2.2.4

Divide

$2 \sqrt{2}$ by

$1$ .

$2 \sqrt{2}$

$2 \sqrt{2}$

$2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$

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