Find the geometric mean between 5 and 12

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.