Introduction

This lesson of Chapter 4 of "Geometry" will introduce you to "Geometric Mean". For more info on this topic, see the wikipedia article, w:Geometric Mean.

Geometric Mean

The Geometric Mean is an "average formula" where two numbers or three numbers are multiplied together. We then find the square root, for two numbers, or the cube root, for three numbers. The "Geometric Mean" requires a proficient understanding of radicals and simplify radicals.

Let's find the Geometric Mean of ${\displaystyle 13}$ and ${\displaystyle 25}$.

1. ${\displaystyle {\tfrac {13}{x}}=}$ • ${\displaystyle {\tfrac {x}{25}}=}$

Make sure the two numbers are multiplied and the two "x"es are multiplied

1. • ${\displaystyle 13}$ • ${\displaystyle 25}$ = ${\displaystyle 325}$
2. Find the square root of both factors.
   • √${\displaystyle x}$² ${\displaystyle =}$ √${\displaystyle 325}$
3. After simplifying our roots, we get: ${\displaystyle x}$ ${\displaystyle =}$ ${\displaystyle 5}$√${\displaystyle 13}$

Answer: The Geometric Mean between ${\displaystyle 13}$ and ${\displaystyle 25}$ is ${\displaystyle 5}$√${\displaystyle 13}$.