Finite Math Examples

$2$ , $12$ , $72$ , $432$

Step 1

Use the formula to find the geometric mean.

$\sqrt[4]{2 \cdot 12 \cdot 72 \cdot 432}$

Step 2

Multiply $2$ by $12$ .

$\sqrt[4]{24 \cdot 72 \cdot 432}$

Step 3

Multiply $24$ by $72$ .

$\sqrt[4]{1728 \cdot 432}$

Step 4

Multiply $1728$ by $432$ .

$\sqrt[4]{746496}$

Step 5

Rewrite $746496$ as $12^{4} \cdot 36$ .

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Step 5.1

Factor $20736$ out of $746496$ .

$\sqrt[4]{20736 (36)}$

Step 5.2

Rewrite $20736$ as $12^{4}$ .

$\sqrt[4]{12^{4} \cdot 36}$

Step 6

Pull terms out from under the radical.

$12 \sqrt[4]{36}$

Step 7

Rewrite $36$ as $6^{2}$ .

$12 \sqrt[4]{6^{2}}$

Step 8

Rewrite $\sqrt[4]{6^{2}}$ as $\sqrt{\sqrt{6^{2}}}$ .

$12 \sqrt{\sqrt{6^{2}}}$

Step 9

Pull terms out from under the radical, assuming positive real numbers.

$12 \sqrt{6}$

Step 10

Approximate the result.

$29.39387691$

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.

$29.4$