Page 355 - Basic College Mathematics with Early Integers

332 C HAPTE R 4 I DECIMALS

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PRACTICE 3 Example 3 Find:
A25
9
Find: 4 2 2 2 4
A16 Solution: = because # =
A25 5 5 5 25
Work Practice 3
Objective Approximating Square Roots

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Thus far, we have found square roots of perfect squares. Numbers like , 36, , and
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1 are called perfect squares because their square roots are whole numbers or frac-
tions. A square root such as 15 cannot be written as a whole number or a fraction
since 5 is not a perfect square.
Although 15 cannot be written as a whole number or a fraction, it can be approx-
imated by estimating, by using a table (as in the appendix), or by using a calculator.
PRACTICE 4 Example 4 Use Appendix A.6 or a calculator to approximate each square
Use Appendix A.6 or a root to the nearest thousandth.
calculator to approximate each
square root to the nearest a. 143 L 6.557 is approximately
thousandth. b. 180 L 8.944
a. 221 b. 255
Work Practice 4

180 , above, is approximately 8.944.This means that if we multiply 8.944 by 8.944,
the product is close to 80.
8.944 * 8.944 L 79.995

It is possible to approximate a square root to the nearest whole number without the
use of a calculator or table.To do so, study the number line below and look for patterns.
PRACTICE 5
25 31 36 40 49 59 64 72 81
Without a calculator or table,
approximate 162 to the 5 6 7 8 9
nearest whole.
Above the number line, notice that as the numbers under the radical signs increase,
their values, and thus their placements on the number line, increase also.

Example 5 Without a calculator or table:

a. Determine which two whole numbers 178 is between.
b. Use part a to approximate 178 to the nearest whole.

Solution:
a. Review perfect squares and recall that 164 = 8 and 181 = 9 . Since 78 is
between 64 and 81, 178 is between 164 (or 8) and 181 (or 9).
78
64 81

8 9 Copyright 2012 Pearson Education, Inc.
Thus, 178 is between 8 and 9.
Answers b. Since 78 is closer to 81,then (as our number line shows) 178 is closer to181 ,or 9.
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3. 4. a. 4.583 b. 7.416 5. 8 Work Practice 5
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