Exercise 28 Page 465

The geometric mean is a mean or average that indicates the central tendency or typical value of a set of numbers. Unlike the arithmetic mean, the geometric mean calculates the $n\text{th}$ root of the product of $n$ values. For example, the geometric mean of $2,$ $4,$ and $8$ is the cube root of the product of $2,$ $4,$ and $8.$ Calculating the geometric mean of two values can be interpreted as calculating the side length of a square with the same area as a rectangle whose dimensions are the given values. For example, consider calculating the geometric mean of $2$ and $4.5.$ The side length $s$ of the square can be calculated by taking the square root of the area. Therefore, the geometric mean of $2$ and $4.5$ is $3,$ which is the side length of the square.