3125 , 2180 , 147

Factor 25 out of 125.

325(5),2180,147

Rewrite 25 as 52.

352⋅5,2180,147

352⋅5,2180,147

Pull terms out from under the radical.

3(55),2180,147

Multiply 5 by 3.

155,2180,147

Factor 36 out of 180.

155,236(5),147

Rewrite 36 as 62.

155,262⋅5,147

155,262⋅5,147

Pull terms out from under the radical.

155,2(65),147

Multiply 6 by 2.

155,125,147

Factor 49 out of 147.

155,125,49(3)

Rewrite 49 as 72.

155,125,72⋅3

155,125,72⋅3

Pull terms out from under the radical.

155,125,73

Use the formula to find the geometric mean.

155⋅(125)⋅(73)3

Multiply 12 by 15.

1805⋅5⋅733

Multiply 7 by 180.

12605⋅533

Raise 5 to the power of 1.

1260(515)33

Raise 5 to the power of 1.

1260(5151)33

Use the power rule aman=am+n to combine exponents.

126051+133

Add 1 and 1.

12605233

Use axn=axn to rewrite 5 as 512.

1260(512)233

Apply the power rule and multiply exponents, (am)n=amn.

1260⋅512⋅233

Combine 12 and 2.

1260⋅52233

Cancel the common factor of 2.

Cancel the common factor.

1260⋅52233

Divide 1 by 1.

1260⋅5133

1260⋅5133

Evaluate the exponent.

1260⋅533

1260⋅533

Multiply 1260 by 5.

630033

Approximate the result.

22.18028176

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.

22.2

Find the Geometric Mean 3 square root of 125 , 2 square root of 180 , square root of 147