For any two positive numbers a and b, the geometric mean is the positive number x such that ax= xb .
sqrt(14)
Practice makes perfect
For any two positive numbers a and b, the geometric mean is the positive number x such that the following equation holds true.
a/x=x/bWe are asked to find the geometric mean of the given pair of numbers.
sqrt(28) and sqrt(7)
Let's substitute them into the equation and use the Cross Product Property to find the mean x.
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 nth root of the product of n values.
Geometric Mean=sqrt(a_1* a_2* ... * a_n)
For example, the geometric mean of 2, 4, and 8 is the cube root of the product of 2, 4, and 8.
sqrt(2*4*8)=sqrt(64)=4
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.
