Exercise 3 Page 623

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. 40 and 15 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x=sqrt(40* 15)

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Evaluate

SplitIntoFactors

Split into factors

x= sqrt(4 * 5 * 2 * 5 * 3)

CommutativePropMult

Commutative Property of Multiplication

x= sqrt(4 * 5 * 5 * 2 * 3)

SqrtProd

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

x= sqrt(4) * sqrt(5 * 5) * sqrt(2 * 3)

Multiply

Multiply

x= sqrt(4) * sqrt(25) * sqrt(6)

CalcRoot

Calculate root

x= 2 * 5 * sqrt(6)

Multiply

Multiply

x = 10sqrt(6)

Using a calculator, we can see that the obtained number is approximately 24.5.