Finite Math Examples

$s = \sqrt{\frac{242}{20 - 1}}$

Step 1

Subtract $1$ from $20$ .

$s = \sqrt{\frac{242}{19}}$

Step 2

Rewrite $\sqrt{\frac{242}{19}}$ as $\frac{\sqrt{242}}{\sqrt{19}}$ .

$s = \frac{\sqrt{242}}{\sqrt{19}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $242$ as $11^{2} \cdot 2$ .

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Step 3.1.1

Factor $121$ out of $242$ .

$s = \frac{\sqrt{121 (2)}}{\sqrt{19}}$

Step 3.1.2

Rewrite $121$ as $11^{2}$ .

$s = \frac{\sqrt{11^{2} \cdot 2}}{\sqrt{19}}$

Step 3.2

Pull terms out from under the radical.

$s = \frac{11 \sqrt{2}}{\sqrt{19}}$

Step 4

Multiply $\frac{11 \sqrt{2}}{\sqrt{19}}$ by $\frac{\sqrt{19}}{\sqrt{19}}$ .

$s = \frac{11 \sqrt{2}}{\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{11 \sqrt{2}}{\sqrt{19}}$ by $\frac{\sqrt{19}}{\sqrt{19}}$ .

$s = \frac{11 \sqrt{2} \sqrt{19}}{\sqrt{19} \sqrt{19}}$

Step 5.2

Raise $\sqrt{19}$ to the power of $1$ .

$s = \frac{11 \sqrt{2} \sqrt{19}}{{\sqrt{19}}^{1} \sqrt{19}}$

Step 5.3

Raise $\sqrt{19}$ to the power of $1$ .

$s = \frac{11 \sqrt{2} \sqrt{19}}{{\sqrt{19}}^{1} {\sqrt{19}}^{1}}$

Step 5.4

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

$s = \frac{11 \sqrt{2} \sqrt{19}}{{\sqrt{19}}^{1 + 1}}$

Step 5.5

Add $1$ and $1$ .

$s = \frac{11 \sqrt{2} \sqrt{19}}{{\sqrt{19}}^{2}}$

Step 5.6

Rewrite ${\sqrt{19}}^{2}$ as $19$ .

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Step 5.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{19}$ as $19^{\frac{1}{2}}$ .

$s = \frac{11 \sqrt{2} \sqrt{19}}{{(19^{\frac{1}{2}})}^{2}}$

Step 5.6.2

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

$s = \frac{11 \sqrt{2} \sqrt{19}}{19^{\frac{1}{2} \cdot 2}}$

Step 5.6.3

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

$s = \frac{11 \sqrt{2} \sqrt{19}}{19^{\frac{2}{2}}}$

Step 5.6.4

Cancel the common factor of $2$ .

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Step 5.6.4.1

Cancel the common factor.

$s = \frac{11 \sqrt{2} \sqrt{19}}{19^{\frac{2}{2}}}$

Step 5.6.4.2

Rewrite the expression.

$s = \frac{11 \sqrt{2} \sqrt{19}}{19^{1}}$

Step 5.6.5

Evaluate the exponent.

$s = \frac{11 \sqrt{2} \sqrt{19}}{19}$

Step 6

Simplify the numerator.

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Step 6.1

Combine using the product rule for radicals.

$s = \frac{11 \sqrt{19 \cdot 2}}{19}$

Step 6.2

Multiply $19$ by $2$ .

$s = \frac{11 \sqrt{38}}{19}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$s = \frac{11 \sqrt{38}}{19}$

Decimal Form:

$s = 3.56887126 \dots$