Finite Math Examples

$\frac{\sqrt{n}}{\sqrt{112}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $112$ as $4^{2} \cdot 7$ .

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Step 1.1.1

Factor $16$ out of $112$ .

$\frac{\sqrt{n}}{\sqrt{16 (7)}}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{n}}{\sqrt{4^{2} \cdot 7}}$

Step 1.2

Pull terms out from under the radical.

$\frac{\sqrt{n}}{4 \sqrt{7}}$

Step 2

Multiply $\frac{\sqrt{n}}{4 \sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt{n}}{4 \sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{\sqrt{n}}{4 \sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt{n} \sqrt{7}}{4 \sqrt{7} \sqrt{7}}$

Step 3.2

Move $\sqrt{7}$ .

$\frac{\sqrt{n} \sqrt{7}}{4 (\sqrt{7} \sqrt{7})}$

Step 3.3

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\sqrt{n} \sqrt{7}}{4 ({\sqrt{7}}^{1} \sqrt{7})}$

Step 3.4

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\sqrt{n} \sqrt{7}}{4 ({\sqrt{7}}^{1} {\sqrt{7}}^{1})}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{n} \sqrt{7}}{4 {\sqrt{7}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{\sqrt{n} \sqrt{7}}{4 {\sqrt{7}}^{2}}$

Step 3.7

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{\sqrt{n} \sqrt{7}}{4 {(7^{\frac{1}{2}})}^{2}}$

Step 3.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{n} \sqrt{7}}{4 \cdot 7^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{n} \sqrt{7}}{4 \cdot 7^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of $2$ .

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Step 3.7.4.1

Cancel the common factor.

$\frac{\sqrt{n} \sqrt{7}}{4 \cdot 7^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$\frac{\sqrt{n} \sqrt{7}}{4 \cdot 7^{1}}$

Step 3.7.5

Evaluate the exponent.

$\frac{\sqrt{n} \sqrt{7}}{4 \cdot 7}$

Step 4

Combine using the product rule for radicals.

$\frac{\sqrt{n \cdot 7}}{4 \cdot 7}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $4$ by $7$ .

$\frac{\sqrt{n \cdot 7}}{28}$

Step 5.2

Reorder factors in $\frac{\sqrt{n \cdot 7}}{28}$ .

$\frac{\sqrt{7 n}}{28}$