Page 109 - Basic College Mathematics with Early Integers

86 C HAPTE R 1 I THE WHOLE NUMBERS

Example 8 illustrates an important property: An exponent applies only to its
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2
base.The exponent 2, in 5 6 , applies only to its base, 6.

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An exponent applies only to its base. For example, 4 2 3 means 4 2 2 2.

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4
Don’t forget that 2 , for example, is not 2 4. The expression 2 4 means repeated
multiplication of the same factor.
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4
2 = 2 2 2 2 = 16, whereas 2 4 = 8

Concept Check Which of the following statements is correct?
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a. 3 6 is the same as 6 6 6.
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b. “Eight to the fourth power” is the same as 8 .
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c. “Ten squared” is the same as 10 .
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d. 11 2 is the same as 11 2.
Objective Evaluating Square Roots

A square root of a number is one of two identical factors of the number. For
example,
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7 7 = 49, so a square root of 49 is 7.
We use this symbol 2 (called a radical sign) for finding square roots. Since
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7 7 = 49, then 249 = 7.

PRACTICE 9–11 Examples Find each square root.
Find each square root.
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9. 225 = 5 because 5 5 = 25
9. 2100 10. 281 = 9 because 9 9 = 81
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10. 24 11. 20 = 0 because 0 0 = 0
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11. 21
Work Practice 9–11

Make sure you understand the difference between squaring a number and finding
the square root of a number.
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2
9 = 9 9 = 81 29 = 3 because 3 3 = 9
Copyright 2012 Pearson Education, Inc.
Not every square root simplifies to a whole number. We will study this more in
a later chapter. In this section, we will find square roots of perfect squares only.
Answers
9. 10 10. 2 11. 1

Concept Check Answer
b