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find the geometric mean of 5 and 12

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The geometric mean of a set of numbers, (a1, a2, ..., an) is defined as the nth root of the product of the numbers, that is:
(a1*a2* ... *an)1/n
In your problem, we have two numbers, (5, 12), so n = 2.  The geometric mean, then, is:
(5*12)1/2  = √60
You can simplify the answer a bit.