Basic Math Examples

65

$65$ ,

63

$63$ ,

78

$78$ ,

63

$63$ ,

69

$69$

Step 1

Use the formula to find the geometric mean.

\sqrt[5]{65 \cdot 63 \cdot 78 \cdot 63 \cdot 69}

$\sqrt[5]{65 \cdot 63 \cdot 78 \cdot 63 \cdot 69}$

Step 2

Multiply

65

$65$ by

63

$63$ .

\sqrt[5]{4095 \cdot 78 \cdot 63 \cdot 69}

$\sqrt[5]{4095 \cdot 78 \cdot 63 \cdot 69}$

Step 3

Multiply

4095

$4095$ by

78

$78$ .

\sqrt[5]{319410 \cdot 63 \cdot 69}

$\sqrt[5]{319410 \cdot 63 \cdot 69}$

Step 4

Multiply

319410

$319410$ by

63

$63$ .

\sqrt[5]{20122830 \cdot 69}

$\sqrt[5]{20122830 \cdot 69}$

Step 5

Multiply

20122830

$20122830$ by

69

$69$ .

\sqrt[5]{1388475270}

$\sqrt[5]{1388475270}$

Step 6

Rewrite

1388475270

$1388475270$ as

3^{5} \cdot 5713890

$3^{5} \cdot 5713890$ .

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Step 6.1

Factor

243

$243$ out of

1388475270

$1388475270$ .

\sqrt[5]{243 (5713890)}

$\sqrt[5]{243 (5713890)}$

Step 6.2

Rewrite

243

$243$ as

3^{5}

$3^{5}$ .

\sqrt[5]{3^{5} \cdot 5713890}

$\sqrt[5]{3^{5} \cdot 5713890}$

Step 7

Pull terms out from under the radical.

$3 \sqrt[5]{5713890}$

Step 8

Approximate the result.

$67.37637322$

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.

$67.4$