# What is the geometric mean of 8 and 18?

Apr 18, 2016

$12$

#### Explanation:

The geometric mean of two positive numbers $a$ and $b$ is $\sqrt{a b}$. The ratio $a : \sqrt{a b}$ is equal to the ratio $\sqrt{a b} : b$.

So the geometric mean of $8$ and $18$ is:

$\sqrt{8 \cdot 18} = \sqrt{144} = 12$

Notice that $\frac{12}{8} = \frac{3}{2} = \frac{18}{12}$