find the geometric mean of 5 and 12

The geometric mean of a set of numbers, (a

_{1}, a_{2}, ..., a_{n}) is defined as the nth root of the product of the numbers, that is:(a

_{1}*a_{2}* ... *a_{n})^{1/n}In your problem, we have two numbers, (5, 12), so n = 2. The geometric mean, then, is:

(5*12)

^{1/2}= √60You can simplify the answer a bit.