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As another example, the geometric mean of 1, ?, and ? is the cube root (i.e., the third root) of their product (0.125), which is ?.
The geometric mean can be understood in terms of geometry. The geometric mean of two numbers, a and b, is simply the side length of the square whose area is equal to that of a rectangle with side lengths a and b. That is, what is n such that n? = a ? b? Similarly, the geometric mean of three numbers, a, b, and c, is the side length of a cube whose volume is the same as that of a rectangular prism with side lengths equal to the three given numbers.
The geometric mean only applies to positive numbers...
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