Basic Math Examples

$\frac{7320 - 7500}{\frac{302}{\sqrt{52}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(7320 - 7500) \frac{\sqrt{52}}{302}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $52$ as $2^{2} \cdot 13$ .

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Step 2.1.1

Factor $4$ out of $52$ .

$(7320 - 7500) \frac{\sqrt{4 (13)}}{302}$

Step 2.1.2

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

$(7320 - 7500) \frac{\sqrt{2^{2} \cdot 13}}{302}$

$(7320 - 7500) \frac{\sqrt{2^{2} \cdot 13}}{302}$

Step 2.2

Pull terms out from under the radical.

$(7320 - 7500) \frac{2 \sqrt{13}}{302}$

$(7320 - 7500) \frac{2 \sqrt{13}}{302}$

Step 3

Simplify terms.

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Step 3.1

Subtract $7500$ from $7320$ .

$- 180 \frac{2 \sqrt{13}}{302}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $- 180$ .

$2 (- 90) \frac{2 \sqrt{13}}{302}$

Step 3.2.2

Factor $2$ out of $302$ .

$2 \cdot - 90 \frac{2 \sqrt{13}}{2 \cdot 151}$

Step 3.2.3

Cancel the common factor.

$2 \cdot - 90 \frac{2 \sqrt{13}}{2 \cdot 151}$

Step 3.2.4

Rewrite the expression.

$- 90 \frac{2 \sqrt{13}}{151}$

$- 90 \frac{2 \sqrt{13}}{151}$

Step 3.3

Combine $- 90$ and $\frac{2 \sqrt{13}}{151}$ .

$\frac{- 90 (2 \sqrt{13})}{151}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Multiply $2$ by $- 90$ .

$\frac{- 180 \sqrt{13}}{151}$

Step 3.4.2

Move the negative in front of the fraction.

$- \frac{180 \sqrt{13}}{151}$

$- \frac{180 \sqrt{13}}{151}$

$- \frac{180 \sqrt{13}}{151}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{180 \sqrt{13}}{151}$

Decimal Form:

$- 4.29800814 \dots$

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