2-3 Perfect Squares and Square Roots
Name
Date
Squaring a number and finding the square root of a number are inverse operations.
To square a number, multiply the
number by itself.
72 # 7 • 7 # 49
The number 49 is called a perfect square
because it is the square of a natural
number.
Simplify: (2 $ 7)2 $ 32
# (9)2 $ 32
Add inside ().
# 81 $ 9
Find each square.
# 90
Add.
So (2 $
7)2
$
32
Find the square root of 81.
(9)(9) # 81 and (!9)( !9) # 81, so both !9 and 9 are
square roots of 81.
81 # 9 is read “the principal square root of 81 is 9.”
! 81 # !9 is read “the negative square root of 81 is !9.”
Simplify 16 ! 2 # 4 ! 2
36 ! 4 6 ! 4
#2
2
#1
So 16 ! 2 simplifies to 1.
36 ! 4
simplified is 90.
Find each square root.
Subtract.
Simplify.
Square each number.
1. 5
2. 7
3. !12
52 " 5 • 5 " 25
5. 27
49
6. ! 45
Copyright © by William H. Sadlier, Inc. All rights reserved.
1,210,000
21. 1.2 " 105
(1.2 # 105)(1.2 # 105)
1.44 # 1010 or
14,400,000,000
0.0004
15. 600
0.0001
6400
18. !1.1
14,400
360,000
1.21
4.9 # 10!5 or
0.000049
0.0016
16. !120
19. !1.3
22. 7 " 10!3
9
16
12. !0.04
0.64
14. 80
17. 1100
36
49
11. 0.02
0.81
1
8. 34
16
25
10. 0.8
13. 0.01
144
7. 67
4
49
9. 0.9
4. !1
20. 1.7
1.69
23. 4 " 102
1.6 # 105 or
160,000
Lesson 2-3, pages 40–41.
2.89
24. 6.5 " 10!1
4.225 # 10!1 or
0.4225
Chapter 2
43
For More Practice Go To:
Find the principal square root.
25.
26. 100
25
5
30.
35.
1
4
10
31.
1
2
1
9
49
27. 121
28. 144
11
32.
1
3
16
25
33.
4
5
2.25
36. 1.96
37. 2.89
1.5
1.4
1.7
38.
16
29. 225
7
12
4
15
0.36
34. 1.69
0.6
1.3
9.61
39.
3.61
1.9
3.1
Simplify each expression.
40. (0.06)2 $ 169
(0.06 • 0.06) $ 13
0.0036 $ 13 " 13.0036
43. ( 34 ) !
2
324
7
!17
16
46. 36 $ (12 $ 7)2
2
120
3
25
44. 121
$ 49
45.
5
7
11
400
!168
2
5
! 64
13.26
48.
1.96 $ (0.02)2
1.4004
50. (3.4)2 $ 2.89
!2.09
100
25
3
4
!6
47. 144 ! (4 $ 9)2
367
49. (! 2.56 ! (0.7)2)
42. (!11)2 ! ( 12 )
41. 144 ! 32
51.
36 ! 1
196 $ 1 1
3
52. A number is squared, and the result is
doubled. The final result is 72. Find the
original number.
53. Three times the square root of a number
is 15. Find the number.
72
2 " 36; 36 " 6
The original number is 6.
15
" 5; 52 " 25
3
The number is 25.
54. What two perfect squares have a difference
that is also a perfect square?
55. Nadine says that the sum of the square roots
of a number is always 0. Do you agree with
Nadine? Explain your answer.
Answers may vary. Possible response:
100 and 64; 100 ! 64 " 36
36 is a perfect square.
Yes; the principal square root and the
negative square root of a number
are opposites.
44
Chapter 2
Copyright © by William H. Sadlier, Inc. All rights reserved.
Solve. Check to justify your answer.