The geometric mean of numbers a and b is the square root of their product (i.e. √(ab)). For example, the geometric mean of 2 and 8 is √(2*8)=4.
Two integers (a and b) are randomly (and independently) chosen between 1 and n (inclusive) where n is an integer greater than one. Create a function that takes a number n as an argument and returns the probability that the geometric mean of a and b is an integer.
f(2) ➞ 0.5
// There are four possible pairs: (1, 1), (2, 1), (1, 2) and (2, 2).
// The pairs (1, 1) and (2, 2) are wanted (√(1*1)=1 and √(2*2)=2)
// but the pairs (2, 1) and (1, 2) are not (√(2*1)=√2 and √(1*2)=√2).
// Thus, the probability is 2/4 = 0.5.
f(10) ➞ 0.18
f(100) ➞ 0.031
Do not round your answer.