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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Geometric Mean

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Exercise 3 Page 623

For any two positive numbers $a$ and $b,$ the geometric mean is the positive number $x$ such that $\frac{a}{x} = \frac{x}{b} .$

$106$ or $24.5$

Practice makes perfect

For any two positive numbers

a

and

b,

the geometric mean is the positive number

x

such that

\frac{a}{x} = \frac{x}{b} .

Since we know that

x

must be positive, the following equation is the definition of a geometric mean.

x = a b

We are asked to find the geometric mean of the given pair of numbers.

40 and 15

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

x .

x = 40 \cdot 15

▼

Evaluate

SplitIntoFactors

Split into factors

x = 4 \cdot 5 \cdot 2 \cdot 5 \cdot 3

CommutativePropMult

Commutative Property of Multiplication

x = 4 \cdot 5 \cdot 5 \cdot 2 \cdot 3

$a \cdot b = a \cdot b$

x = 4 \cdot 5 \cdot 5 \cdot 2 \cdot 3

Multiply

x = 4 \cdot 25 \cdot 6

Calculate root

x = 2 \cdot 5 \cdot 6

Multiply

x = 106

Using a calculator, we can see that the obtained number is approximately

24.5 .

Subchapter links

Exercises p.623-627