Basic Math Examples

41

$41$ ,

138 \div 302

$138 \div 302$

Step 1

Rewrite the division as a fraction.

41, \frac{138}{302}

$41, \frac{138}{302}$

Step 2

Cancel the common factor of

138

$138$ and

302

$302$ .

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Step 2.1

Factor

2

$2$ out of

138

$138$ .

41, \frac{2 (69)}{302}

$41, \frac{2 (69)}{302}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

2

$2$ out of

302

$302$ .

41, \frac{2 \cdot 69}{2 \cdot 151}

$41, \frac{2 \cdot 69}{2 \cdot 151}$

Step 2.2.2

Cancel the common factor.

$41, \frac{2 \cdot 69}{2 \cdot 151}$

Step 2.2.3

Rewrite the expression.

$41, \frac{69}{151}$

Step 3

Use the formula to find the geometric mean.

$\sqrt{41 \cdot \frac{69}{151}}$

Step 4

Combine

$41$ and

$\frac{69}{151}$ .

$\sqrt{\frac{41 \cdot 69}{151}}$

Step 5

Multiply

$41$ by

$69$ .

$\sqrt{\frac{2829}{151}}$

Step 6

Rewrite

$\sqrt{\frac{2829}{151}}$ as

$\frac{\sqrt{2829}}{\sqrt{151}}$ .

$\frac{\sqrt{2829}}{\sqrt{151}}$

Step 7

Multiply

$\frac{\sqrt{2829}}{\sqrt{151}}$ by

$\frac{\sqrt{151}}{\sqrt{151}}$ .

$\frac{\sqrt{2829}}{\sqrt{151}} \cdot \frac{\sqrt{151}}{\sqrt{151}}$

Step 8

Combine and simplify the denominator.

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Step 8.1

Multiply

$\frac{\sqrt{2829}}{\sqrt{151}}$ by

$\frac{\sqrt{151}}{\sqrt{151}}$ .

$\frac{\sqrt{2829} \sqrt{151}}{\sqrt{151} \sqrt{151}}$

Step 8.2

Raise

$\sqrt{151}$ to the power of

$1$ .

$\frac{\sqrt{2829} \sqrt{151}}{{\sqrt{151}}^{1} \sqrt{151}}$

Step 8.3

Raise

$\sqrt{151}$ to the power of

$1$ .

$\frac{\sqrt{2829} \sqrt{151}}{{\sqrt{151}}^{1} {\sqrt{151}}^{1}}$

Step 8.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{2829} \sqrt{151}}{{\sqrt{151}}^{1 + 1}}$

Step 8.5

Add

$1$ and

$1$ .

$\frac{\sqrt{2829} \sqrt{151}}{{\sqrt{151}}^{2}}$

Step 8.6

Rewrite

${\sqrt{151}}^{2}$ as

$151$ .

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Step 8.6.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{151}$ as

$151^{\frac{1}{2}}$ .

$\frac{\sqrt{2829} \sqrt{151}}{{(151^{\frac{1}{2}})}^{2}}$

Step 8.6.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{2829} \sqrt{151}}{151^{\frac{1}{2} \cdot 2}}$

Step 8.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{\sqrt{2829} \sqrt{151}}{151^{\frac{2}{2}}}$

Step 8.6.4

Cancel the common factor of

$2$ .

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Step 8.6.4.1

Cancel the common factor.

$\frac{\sqrt{2829} \sqrt{151}}{151^{\frac{2}{2}}}$

Step 8.6.4.2

Rewrite the expression.

$\frac{\sqrt{2829} \sqrt{151}}{151^{1}}$

Step 8.6.5

Evaluate the exponent.

$\frac{\sqrt{2829} \sqrt{151}}{151}$

Step 9

Simplify the numerator.

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Step 9.1

Combine using the product rule for radicals.

$\frac{\sqrt{2829 \cdot 151}}{151}$

Step 9.2

Multiply

$2829$ by

$151$ .

$\frac{\sqrt{427179}}{151}$

Step 10

Approximate the result.

$4.32840609$

Step 11

The geometric mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$4.3$