Find the Geometric Mean 1 , 754÷21

$1$ , $754 \div 21$

Step 1

Rewrite the division as a fraction.

$1, \frac{754}{21}$

Step 2

Use the formula to find the geometric mean.

$\sqrt{1 \cdot \frac{754}{21}}$

Step 3

Multiply $\frac{754}{21}$ by $1$ .

$\sqrt{\frac{754}{21}}$

Step 4

Rewrite $\sqrt{\frac{754}{21}}$ as $\frac{\sqrt{754}}{\sqrt{21}}$ .

$\frac{\sqrt{754}}{\sqrt{21}}$

Step 5

Multiply $\frac{\sqrt{754}}{\sqrt{21}}$ by $\frac{\sqrt{21}}{\sqrt{21}}$ .

$\frac{\sqrt{754}}{\sqrt{21}} \cdot \frac{\sqrt{21}}{\sqrt{21}}$

Step 6

Combine and simplify the denominator.

Multiply $\frac{\sqrt{754}}{\sqrt{21}}$ by $\frac{\sqrt{21}}{\sqrt{21}}$ .

$\frac{\sqrt{754} \sqrt{21}}{\sqrt{21} \sqrt{21}}$

Raise $\sqrt{21}$ to the power of $1$ .

$\frac{\sqrt{754} \sqrt{21}}{{\sqrt{21}}^{1} \sqrt{21}}$

Raise $\sqrt{21}$ to the power of $1$ .

$\frac{\sqrt{754} \sqrt{21}}{{\sqrt{21}}^{1} {\sqrt{21}}^{1}}$

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

$\frac{\sqrt{754} \sqrt{21}}{{\sqrt{21}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{754} \sqrt{21}}{{\sqrt{21}}^{2}}$

Rewrite ${\sqrt{21}}^{2}$ as $21$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{21}$ as $21^{\frac{1}{2}}$ .

$\frac{\sqrt{754} \sqrt{21}}{{(21^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{754} \sqrt{21}}{21^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{754} \sqrt{21}}{21^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{754} \sqrt{21}}{21^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{754} \sqrt{21}}{21^{1}}$

Evaluate the exponent.

$\frac{\sqrt{754} \sqrt{21}}{21}$

Step 7

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{754 \cdot 21}}{21}$

Multiply $754$ by $21$ .

$\frac{\sqrt{15834}}{21}$

Step 8

Approximate the result.

$5.99205823$

Step 9

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.

$6$

Find the Geometric Mean 1 , 754÷21

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