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McGraw Hill Integrated II, 2012 View details

1. Geometric Mean

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Exercise 28 Page 624

For any two positive numbers a and b, the geometric mean is the positive number x such that ax= xb .

5sqrt(3)/4 or 2.2

Practice makes perfect

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. 3sqrt(5)/4 and 5sqrt(5)/4 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

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

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Evaluate

MultFrac

Multiply fractions

x=sqrt(15 * sqrt(5) * sqrt(5)/16)

MultSqrt

sqrt(a)* sqrt(a)= a

x=sqrt(15 * 5/16)

Multiply

x=sqrt(75/16)

SqrtQuot