Exercise 59 Page 637

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. 12 and 15 Let's substitute them into the equation and simplify the right-hand side to find the mean x.

x = sqrt(ab)

SubstituteII

a= 12, b= 15

x = sqrt(12 * 15)

▼

Evaluate right-hand side

Multiply

Multiply

x = sqrt(180)

CalcRoot

Calculate root

x = 6sqrt(5)

UseCalc

Use a calculator

x = 13.416407...

RoundDec

Round to 1 decimal place(s)

x ≈ 13.4