Exercise 12 Page 703

For any two positive numbers a and b, the geometric mean is the positive number x such that ax= x b. 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. sqrt(20) and sqrt(80) Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x=sqrt(sqrt(20) * sqrt(80))

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Simplify

ProdSqrt

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

x=sqrt(sqrt(20 * 80))

Multiply

Multiply

x=sqrt(sqrt(1600))

CalcRoot

Calculate root

x=sqrt(40)

SplitIntoFactors

Split into factors

x=sqrt(4* 10)

SqrtProd

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

x=sqrt(4)* sqrt(10)

CalcRoot

Calculate root

x=2sqrt(10)