# Find the Geometric Mean 7/15*5 , 2

715⋅5 , 2
Cancel the common factor of 5.
Factor 5 out of 15.
75(3)⋅5,2
Cancel the common factor.
75⋅3⋅5,2
Rewrite the expression.
73,2
73,2
Use the formula to find the geometric mean.
73⋅2
Combine 73 and 2.
7⋅23
Multiply 7 by 2.
143
Rewrite 143 as 143.
143
Multiply 143 by 33.
143⋅33
Combine and simplify the denominator.
Multiply 143 and 33.
14333
Raise 3 to the power of 1.
143313
Raise 3 to the power of 1.
1433131
Use the power rule aman=am+n to combine exponents.
14331+1
14332
Rewrite 32 as 3.
Use axn=axn to rewrite 3 as 312.
143(312)2
Apply the power rule and multiply exponents, (am)n=amn.
143312⋅2
Combine 12 and 2.
143322
Cancel the common factor of 2.
Cancel the common factor.
143322
Divide 1 by 1.
14331
14331
Evaluate the exponent.
1433
1433
1433
Simplify the numerator.
Combine using the product rule for radicals.
14⋅33
Multiply 14 by 3.
423
423
Approximate the result.
2.16024689
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.
2.2
Find the Geometric Mean 7/15*5 , 2

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