Exercise 4 Page 661

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

x=sqrt(50* 10)

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Simplify right-hand side

Multiply

Multiply

x=sqrt(500)

SplitIntoFactors

Split into factors

x=sqrt(100(5))

ProdSqrt

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

x=sqrt(100)sqrt(5)

CalcRoot

Calculate root

x=10sqrt(5)