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

Dec 22, 2016

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:

$\sqrt{36} \cdot \sqrt{4} = 6 \cdot 2 = 12$

In general, the geometric mean of $a , b > 0$ is $\sqrt{a b} = \sqrt{a} \sqrt{b}$.

When calculating, just choose which of $\sqrt{a b}$ and $\sqrt{a} \sqrt{b}$ is easiest to work with.