Finite Math Examples

$\frac{\sqrt{360 m n}}{3 \sqrt{5}}$

Step 1

Combine $\sqrt{360 m n}$ and $\sqrt{5}$ into a single radical.

$\frac{\sqrt{\frac{360 m n}{5}}}{3}$

Step 2

Cancel the common factor of $360$ and $5$ .

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Step 2.1

Factor $5$ out of $360 m n$ .

$\frac{\sqrt{\frac{5 (72 m n)}{5}}}{3}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $5$ .

$\frac{\sqrt{\frac{5 (72 m n)}{5 (1)}}}{3}$

Step 2.2.2

Cancel the common factor.

$\frac{\sqrt{\frac{5 (72 m n)}{5 \cdot 1}}}{3}$

Step 2.2.3

Rewrite the expression.

$\frac{\sqrt{\frac{72 m n}{1}}}{3}$

Step 2.2.4

Divide $72 m n$ by $1$ .

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

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

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

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $72 m n$ as $6^{2} \cdot (2 m n)$ .

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Step 3.1.1

Factor $36$ out of $72$ .

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

Step 3.1.2

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

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

Step 3.1.3

Add parentheses.

$\frac{\sqrt{6^{2} \cdot 2 (m n)}}{3}$

Step 3.1.4

Add parentheses.

$\frac{\sqrt{6^{2} \cdot (2 m n)}}{3}$

$\frac{\sqrt{6^{2} \cdot (2 m n)}}{3}$

Step 3.2

Pull terms out from under the radical.

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

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

Step 4

Cancel the common factor of $6$ and $3$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.2.4

Divide $2 \sqrt{2 m n}$ by $1$ .

$2 \sqrt{2 m n}$

$2 \sqrt{2 m n}$

$2 \sqrt{2 m n}$

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