# How do you find the geometric mean between 36 and 24?

Jan 6, 2017

$\textcolor{g r e e n}{12 \sqrt{6}}$

#### Explanation:

The geometric mean of two numbers is
$\textcolor{w h i t e}{\text{XX}}$The square root of
$\textcolor{w h i t e}{\text{XXXX}}$the product of the two numbers:

Therefore the geometric mean of $36$ and $24$ is
$\textcolor{w h i t e}{\text{XXX}} \sqrt{36 \times 24}$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{3 \times 12 \times 2 \times 12}$
$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{12}^{2} \times 3 \times 2}$
$\textcolor{w h i t e}{\text{XXX}} = 12 \sqrt{6}$