Finite Math Examples

$\frac{\sqrt{72} - 15}{3}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.1.1

Factor $36$ out of $72$ .

$\frac{\sqrt{36 (2)} - 15}{3}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

$\frac{\sqrt{6^{2} \cdot 2} - 15}{3}$

$\frac{\sqrt{6^{2} \cdot 2} - 15}{3}$

Step 1.2

Pull terms out from under the radical.

$\frac{6 \sqrt{2} - 15}{3}$

$\frac{6 \sqrt{2} - 15}{3}$

Step 2

Cancel the common factor of $6 \sqrt{2} - 15$ and $3$ .

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Step 2.1

Factor $3$ out of $6 \sqrt{2}$ .

$\frac{3 (2 \sqrt{2}) - 15}{3}$

Step 2.2

Factor $3$ out of $- 15$ .

$\frac{3 (2 \sqrt{2}) + 3 \cdot - 5}{3}$

Step 2.3

Factor $3$ out of $3 (2 \sqrt{2}) + 3 (- 5)$ .

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

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $3$ out of $3$ .

$\frac{3 (2 \sqrt{2} - 5)}{3 (1)}$

Step 2.4.2

Cancel the common factor.

$\frac{3 (2 \sqrt{2} - 5)}{3 \cdot 1}$

Step 2.4.3

Rewrite the expression.

$\frac{2 \sqrt{2} - 5}{1}$

Step 2.4.4

Divide $2 \sqrt{2} - 5$ by $1$ .

$2 \sqrt{2} - 5$

$2 \sqrt{2} - 5$

$2 \sqrt{2} - 5$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2} - 5$

Decimal Form:

$- 2.17157287 \dots$

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