# How do you find the geometric mean between 18 and 1.5?

Feb 6, 2017

$3 \sqrt{3}$ is the geometric mean between $18$ and $1.5$

#### Explanation:

Finding geometric mean between two numbers $a$ and $b$, means identifying a number $x$ so that

$a$, $x$ and $b$ are in geometric sequence

i.e. $\frac{a}{x} = \frac{x}{b}$ or ${x}^{2} = a b$ i.e. $x = \sqrt{a b}$

Hence, geometric mean between $18$ and $1.5$ is

$\sqrt{18 \times 1.5}$

= $\sqrt{27}$

= $3 \sqrt{3}$

Hence, $3 \sqrt{3}$ is the geometric mean between $18$ and $1.5$