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Concept

Geometric Mean

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 root of the product of values.

Geometric Mean

Consider an example where the geometric mean of and is the cube root of the product of and
Additionally, 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. Calculating the geometric mean of and for example, is finding the side length of a square with the same area as a rectangle whose dimensions are and
A rectangle with side lengths 2 and 4.5 (at the left), and a square with side lengths s (at the right). The area of a rectangle calculated as A_1= 2*4.5, and the area of a square is calculated as A_2= s^2. The areas of the rectangle and the square are equal, denoted as A_1=A_2
The side length of the square can be calculated by taking the square root of the area.
Solve for
Evaluate right-hand side
Therefore, the geometric mean of and is which is the side length of the square.