Exercise 10 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. 20 and 25 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x=sqrt(20* 25)

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Evaluate

SplitIntoFactors

Split into factors

x=sqrt(5 * 4 * 25)

CommutativePropMult

Commutative Property of Multiplication

x=sqrt(25 * 4 * 5)

SqrtProd

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

x=sqrt(25)* sqrt(4)*sqrt(5)

CalcRoot

Calculate root

x = 5 * 2 * sqrt(5)

Multiply

Multiply

x= 10sqrt(5)

Using a calculator, we can see that the obtained number is approximately 22.4.