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

3125 , 2180 , 147
Rewrite 125 as 52⋅5.
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
Rewrite 180 as 62⋅5.
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
Rewrite 147 as 72⋅3.
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
12605233
Rewrite 52 as 5.
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