Question

How do you find the geometric mean between 36 and 4?

Answer 1

The geometric mean of `36` and `4` is `12`

Explanation:

Since `36=6^2` and `4=2^2` are both perfect squares, the easiest way is to multiply their square roots:

`sqrt(36)*sqrt(4) = 6*2 = 12`

In general, the geometric mean of `a, b > 0` is `sqrt(ab) = sqrt(a)sqrt(b)`.

When calculating, just choose which of `sqrt(ab)` and `sqrt(a)sqrt(b)` is easiest to work with.