Finite Math Examples

$\frac{725 - 700}{\frac{85}{\sqrt{54}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(725 - 700) \frac{\sqrt{54}}{85}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $54$ as $3^{2} \cdot 6$ .

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Step 2.1.1

Factor $9$ out of $54$ .

$(725 - 700) \frac{\sqrt{9 (6)}}{85}$

Step 2.1.2

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

$(725 - 700) \frac{\sqrt{3^{2} \cdot 6}}{85}$

$(725 - 700) \frac{\sqrt{3^{2} \cdot 6}}{85}$

Step 2.2

Pull terms out from under the radical.

$(725 - 700) \frac{3 \sqrt{6}}{85}$

$(725 - 700) \frac{3 \sqrt{6}}{85}$

Step 3

Simplify terms.

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Step 3.1

Subtract $700$ from $725$ .

$25 \frac{3 \sqrt{6}}{85}$

Step 3.2

Cancel the common factor of $5$ .

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Step 3.2.1

Factor $5$ out of $25$ .

$5 (5) \frac{3 \sqrt{6}}{85}$

Step 3.2.2

Factor $5$ out of $85$ .

$5 \cdot 5 \frac{3 \sqrt{6}}{5 \cdot 17}$

Step 3.2.3

Cancel the common factor.

$5 \cdot 5 \frac{3 \sqrt{6}}{5 \cdot 17}$

Step 3.2.4

Rewrite the expression.

$5 \frac{3 \sqrt{6}}{17}$

$5 \frac{3 \sqrt{6}}{17}$

Step 3.3

Combine $5$ and $\frac{3 \sqrt{6}}{17}$ .

$\frac{5 (3 \sqrt{6})}{17}$

Step 3.4

Multiply $3$ by $5$ .

$\frac{15 \sqrt{6}}{17}$

$\frac{15 \sqrt{6}}{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{15 \sqrt{6}}{17}$

Decimal Form:

$2.16131447 \dots$

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