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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Geometric Mean

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Exercise 2 Page 623

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

12

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 4 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x=sqrt(36* 4)

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Evaluate

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

x= sqrt(36) * sqrt(4)

Calculate root

x= 6 * 2

Multiply

x = 12

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Exercises p.623-627