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

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Answer 1 · 2017-02-06T08:58:06

$3 \sqrt{3}$ $3sqrt3$ is the geometric mean between $18$ $18$ and $1.5$ $1.5$

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

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

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

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

$\sqrt{18 \times 1.5}$ $sqrt(18xx1.5)$

= $\sqrt{27}$ $sqrt27$

= $3 \sqrt{3}$ $3sqrt3$

Hence, $3 \sqrt{3}$ $3sqrt3$ is the geometric mean between $18$ $18$ and $1.5$ $1.5$