Finite Math Examples

$2$ , $12$ , $12$ , $17$ , $17$ , $18$ , $18$ , $21$ , $27$ , $29$

Step 1

Use the formula to find the geometric mean.

$\sqrt[10]{2 \cdot 12 \cdot 12 \cdot 17 \cdot 17 \cdot 18 \cdot 18 \cdot 21 \cdot 27 \cdot 29}$

Step 2

Multiply $2$ by $12$ .

$\sqrt[10]{24 \cdot 12 \cdot 17 \cdot 17 \cdot 18 \cdot 18 \cdot 21 \cdot 27 \cdot 29}$

Step 3

Multiply $24$ by $12$ .

$\sqrt[10]{288 \cdot 17 \cdot 17 \cdot 18 \cdot 18 \cdot 21 \cdot 27 \cdot 29}$

Step 4

Multiply $288$ by $17$ .

$\sqrt[10]{4896 \cdot 17 \cdot 18 \cdot 18 \cdot 21 \cdot 27 \cdot 29}$

Step 5

Multiply $4896$ by $17$ .

$\sqrt[10]{83232 \cdot 18 \cdot 18 \cdot 21 \cdot 27 \cdot 29}$

Step 6

Multiply $83232$ by $18$ .

$\sqrt[10]{1498176 \cdot 18 \cdot 21 \cdot 27 \cdot 29}$

Step 7

Multiply $1498176$ by $18$ .

$\sqrt[10]{26967168 \cdot 21 \cdot 27 \cdot 29}$

Step 8

Multiply $26967168$ by $21$ .

$\sqrt[10]{566310528 \cdot 27 \cdot 29}$

Step 9

Multiply $566310528$ by $27$ .

$\sqrt[10]{15290384256 \cdot 29}$

Step 10

Multiply $15290384256$ by $29$ .

$\sqrt[10]{443421143424}$

Step 11

Rewrite $443421143424$ as $3^{10} \cdot 7509376$ .

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Step 11.1

Factor $59049$ out of $443421143424$ .

$\sqrt[10]{59049 (7509376)}$

Step 11.2

Rewrite $59049$ as $3^{10}$ .

$\sqrt[10]{3^{10} \cdot 7509376}$

Step 12

Pull terms out from under the radical.

$3 \sqrt[10]{7509376}$

Step 13

Approximate the result.

$14.61105715$

Step 14

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.

$14.6$