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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Chapter Review

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Exercise 18 Page 482

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

2sqrt(15)

Practice makes perfect

For any two positive numbers a and b, the geometric mean is the positive number x such that the following equation holds true. a/x=x/bWe are asked to find the geometric mean of the given pair of numbers. 5 and 12 Let's substitute them into the equation and use the Cross Product Property to find the mean x.

5/x=x/12

Cross multiply

x * x = 5 * 12

▼

Solve for x

ProdToPowTwoFac

a* a=a^2

x^2= 5 * 12

Multiply

x^2 = 60

sqrt(LHS)=sqrt(RHS)

sqrt(x^2) = sqrt(60)

SplitIntoFactors

Split into factors

sqrt(x^2) = sqrt(4*15)

Write as a power

sqrt(x^2) = sqrt(2^2*15)

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

sqrt(x^2) = sqrt(2^2)*sqrt(15)

sqrt(a^2)=|a|

|x| = ±sqrt(2^2)*sqrt(15)

SqrtPowToNumber

sqrt(a^2)=a

|x| = ±2sqrt(15)

x ≥ 0

x = 2sqrt(15)