Geometry/Chapter 4/Lesson 7

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 $13$ and $25$.

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

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

Answer: The Geometric Mean between $13$ and $25$ is $5$√$13$.