NAME ______________________________________________ DATE______________ PERIOD _____
1-8
Study Guide and Intervention
Number Systems
Square Roots A square root is one of two equal factors of a number. For example, the
square roots of 36 are 6 and !6, since 6 " 6 or 62 is 36 and (!6)(!6) or (!6)2 is also 36. A
rational number like 36, whose square root is a rational number, is called a perfect
square.
The symbol !" is a radical sign. It indicates the nonnegative, or principal, square root of
36 # 6 and !!36
# # !6. The symbol $!36
#
the number under the radical sign. So !#
represents both square roots.
Find !
!".
Example 2
25
%%
49
$!#
0.16 represents the positive and
negative square roots of 0.16.
0.16 # 0.42 and 0.16 # (!0.4)2
$%
25
%% represents the negative
49
25
square root of %
%.
49
!
& '
25
5 2
%% # %% → !
49
7
Find "#0.16
$.
$!0.16
# # $0.4
$%
25
5
%% # !%%
49
7
Lesson 1-8
Example 1
Exercises
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find each square root.
#
1. !64
2. !!81
#
3. !16.81
#
4. $!100
#
5. !
$%
6. !!121
#
$%
8. !
$%
9. $
7. $
25
%
144
10. !!3600
#
13.
$%
144
%
196
Chapter 1
4
%
25
25
%
16
11. !!6.25
#
14. !
$%
121
%
100
12. $!0.000
#4#
$%
36
%
49
15. $!1.21
#
57
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
1-8
Study Guide and Intervention
(continued)
Number Systems
Classify and Order Numbers Numbers such as !2" and !3" are not perfect squares.
Notice what happens when you find these square roots with your calculator. The numbers
continue indefinitely without any pattern of repeating digits. Numbers that cannot be
written as a terminating or repeating decimal are called irrational numbers. The set of
real numbers consists of the set of irrational numbers and the set of rational numbers
together. The chart below illustrates the various kinds of real numbers.
Natural Numbers
{1, 2, 3, 4, …}
Whole Numbers
{0, 1, 2, 3, 4, …}
Integers
{…, !3, !2, !1, 0, 1, 2, 3, …}
Rational Numbers
{all numbers that can be expressed in the form $ , where a and b are integers and b " 0}
Irrational Numbers
{all numbers that cannot be expressed in the form $ , where a and b are integers and b " 0}
Example
4
11
a
b
a
b
Name the set or sets of numbers to which each real number belongs.
a. !
Because 4 and 11 are integers, this number is a rational number.
"
b. !81
Because !81
" # 9, this number is a natural number, a whole number, an integer,
and a rational number.
c. !32
"
Because !32
" # 5.656854249…, which is not a repeating or terminating decimal,
this number is irrational.
Name the set or sets of numbers to which each real number belongs.
6
7
2
3
1. $
84
12
2. ! $
3. $
"
4. !54
5. 3.145
6. !25
"
7. 0.62626262…
8. !22.51
"
Write each set of numbers in order from least to greatest.
3
4
7
4
", $
9. ! $ , !5, !25
5
4
12. $ , !2, !124
", !3.11
Chapter 1
3
5
10. !0.09
", !0.3131…, $
1
5
13. !!1.44
", !0.35 $
58
1
4
11. !1.2
"5
", 0.05, ! $ , !5
"
1
3
9
5
14. 0.3
"5
", 2 $ , ! $ , !5
"
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises