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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 54 Page 627

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

A

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. 8 and 22 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x=sqrt(8* 22)

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Evaluate

SplitIntoFactors

Split into factors

x = sqrt(4 * 2 * 2 * 11)

Multiply

x = sqrt(4 * 4 * 11)

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

x = sqrt(4) * sqrt(4) * sqrt(11)

Calculate root

x = 2 * 2 * sqrt(11)

Multiply

x= 4sqrt(11)

We can see that the obtained value corresponds to option A.

Subchapter links

Exercises p.623-627