Find the Geometric Mean 1 , 8 , 27 , 64 , 125

$1$ , $8$ , $27$ , $64$ , $125$

Step 1

Use the formula to find the geometric mean.

$\sqrt[5]{1 \cdot 8 \cdot 27 \cdot 64 \cdot 125}$

Step 2

Multiply $8$ by $1$ .

$\sqrt[5]{8 \cdot 27 \cdot 64 \cdot 125}$

Step 3

Multiply $8$ by $27$ .

$\sqrt[5]{216 \cdot 64 \cdot 125}$

Step 4

Multiply $216$ by $64$ .

$\sqrt[5]{13824 \cdot 125}$

Step 5

Multiply $13824$ by $125$ .

$\sqrt[5]{1728000}$

Step 6

Rewrite $1728000$ as $2^{5} \cdot 54000$ .

Factor $32$ out of $1728000$ .

$\sqrt[5]{32 (54000)}$

Rewrite $32$ as $2^{5}$ .

$\sqrt[5]{2^{5} \cdot 54000}$

Step 7

Pull terms out from under the radical.

$2 \sqrt[5]{54000}$

Step 8

Approximate the result.

$17.6810783$

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.

$17.7$

Find the Geometric Mean 1 , 8 , 27 , 64 , 125

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