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McGraw Hill Integrated II, 2012 View details

1. Geometric Mean

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Exercise 11 Page 623

For any two positive numbers a and b, the geometric mean is the positive number x such that ax= xb.

12sqrt(6) ≈ 29.4

Practice makes perfect

For any two positive numbers a and b, the geometric mean is the positive number x such that ax= xb. Since we know that x must be positive, the following equation is the definition of a geometric mean. x= sqrt(a b)We are asked to find the geometric mean of the given pair of numbers. 36 and 24 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x=sqrt(36* 24)

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Evaluate

SplitIntoFactors

Split into factors

x=sqrt(36 * 4 * 6)

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

x=sqrt(36)* sqrt(4)*sqrt(6)

CalcRoot

Calculate root

x= 6 * 2 *sqrt(6)