Find the Geometric Mean 1 , 4 , 9 , 16

$1$ , $4$ , $9$ , $16$

Step 1

Use the formula to find the geometric mean.

$\sqrt[4]{1 \cdot 4 \cdot 9 \cdot 16}$

Step 2

Multiply $4$ by $1$ .

$\sqrt[4]{4 \cdot 9 \cdot 16}$

Step 3

Multiply $4$ by $9$ .

$\sqrt[4]{36 \cdot 16}$

Step 4

Multiply $36$ by $16$ .

$\sqrt[4]{576}$

Step 5

Rewrite $576$ as $2^{4} \cdot 36$ .

Factor $16$ out of $576$ .

$\sqrt[4]{16 (36)}$

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 36}$

Step 6

Pull terms out from under the radical.

$2 \sqrt[4]{36}$

Step 7

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

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

Step 8

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

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

Step 9

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

$2 \sqrt{6}$

Step 10

Approximate the result.

$4.89897948$

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.

$4.9$

Find the Geometric Mean 1 , 4 , 9 , 16

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