Concepts
1 BasicFunctions
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Unit 1C
Review of Operations with
Decimal Fractions and Percent
Copyright © Cengage Learning. All rights reserved.
1.15
Powers and Roots
Copyright © Cengage Learning. All rights reserved.
Powers and Roots
The square of a number is the product of that number
times itself. The square of 3 is 3  3 or 32 or 9.
The square of a number may be found with a calculator as
follows.
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Example 1
Find 73.62 rounded to three significant digits.
Thus, 73.62 = 5420 rounded to three significant digits.
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Powers and Roots
The square root of a number is that positive number
which, when multiplied by itself, gives the original number.
The square root of 25 is 5 and is written as
symbol
is called a radical.
. The
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Example 3
Find the square roots of a. 16, b. 64, c. 100, and d. 144.
a.
= 4 because 4  4 = 16
b.
= 8 because 8  8 = 64
c.
= 10 because 10  10 = 100
d.
= 12 because 12  12 = 144
Numbers whose square roots are whole numbers are
called perfect squares. For example,1, 4, 9, 16, 25, 36,
49, and 64 are perfect squares.
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Powers and Roots
The cube of a number is the product of that number times
itself three times. The cube of 5 is 5  5  5 or 53 or 125.
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Example 6
Find the cubes of a. 2, b. 3, c. 4, and d. 10.
a. 23 = 2  2  2 = 8
b. 33 = 3  3  3 = 27
c. 43 = 4  4  4 = 64
d. 103 = 10  10  10 = 1000
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Powers and Roots
The cube root of a number is that number which, when
multiplied by itself three times, gives the original number.
The cube root of 8 is 2 and is written as
.
(Note: 2  2  2 = 8. The small 3 in the radical is called the
index.)
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Example 9
Find the cube roots of a. 8, b. 27, and c. 125.
a.
= 2 because 2  2  2 = 8
b.
= 3 because 3  3  3 = 27
c.
= 5 because 5  5  5 = 125
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Powers and Roots
Numbers whose cube roots are whole numbers are called
perfect cubes. For example, 1, 8, 27, 64, 125, and 216 are
perfect cubes.
In general, in a power of a number, the exponent indicates
the number of times the base is used as a factor.
For example, the 4th power of 3 is written 34, which means
that 3 is used as a factor 4 times (34 = 3  3  3  3 = 81).
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Example 12
Find 2.245 rounded to three significant digits.
Thus, 2.245 = 56.4 rounded to three significant digits.
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