# How do you find the geometric mean for the pair of numbers: 1/12 , 1/18?

Feb 26, 2016

Multiply the pair of numbers and take their square root to find the geometric mean to be

$\frac{1}{6} \sqrt{\frac{1}{6}} \approx 14.697$

#### Explanation:

The geometric mean of a set of $n$ numbers is the ${n}^{\text{th}}$ root of the product of all of the numbers. In this case, we have two numbers, and thus take the square root of their product.

$\text{geometric mean} = \sqrt{\frac{1}{12} \cdot \frac{1}{18}}$

=sqrt((1/6)^2*1/6

$= \frac{1}{6} \sqrt{\frac{1}{6}} \approx 14.697$