Exercise 13 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. 8sqrt(2)/3 and 4sqrt(2)/3 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x=sqrt(8sqrt(2)/3 * 4sqrt(2)/3)

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Simplify

MultFrac

Multiply fractions

x=sqrt(8sqrt(2)* 4sqrt(2)/3 * 3)

CommutativePropMult

Commutative Property of Multiplication

x=sqrt(8* 4 * sqrt(2)* sqrt(2)/3 * 3)

MultSqrt

sqrt(a)* sqrt(a)= a

x=sqrt(8 * 4 * 2/3 * 3)

Multiply

Multiply

x=sqrt(64/9)

SqrtQuot

sqrt(a/b)=sqrt(a)/sqrt(b)

x=sqrt(64)/sqrt(9)

CalcRoot

Calculate root

x= 8/3