e x p l o r at i o n
Georgia Performance
Standards
4E
Squares and Square
Roots
M8N1.a, M8N1.b,
M8N1.d, M8N1.e
The sequence shows the square numbers 1, 4, 9, and 16.
42 16
32 9
22 4
12 1
13
1
3
135
1357
1. Draw a picture to show that 52 1 3 5 7 9.
2. Add the odd numbers 1 3 5 7 9 ... 17 19.
What square number do you get?
3. The table starts with 112 1 3 5 7 9 11 13 15 17 19 21 121. Complete the table by adding
the next odd number to this sum.
112
122
132
142
152
162
172
182
192
202
121
Think and Discuss
4. Explain how you can determine square numbers using
sums of odd numbers.
5. Demonstrate that the value of 222 can be determined by
adding odd numbers.
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Holt Mathematics
Name
LESSON
4E
Date
Class
Review for Mastery
Squares and Square Roots
A perfect square has two identical factors.
25 5 5 52 or 25 (5) (5) (5)2 then 25 is a perfect square.
Tell if the number is a perfect square.
If yes, write its identical factors.
1. 121
2. 200
3. 400
25
5 and 25
5
Since 52 25 and also (5)2 25,
both 5 and 5 are square roots of 25.
The principal square root of 25 is 5: 25
5
Write the two square roots of each number.
4. 81
5. 625
81
6. 169
625
169
Write the principal square root of each number.
7. 144
8. 6400
Use the principal square root when
evaluating an expression. For the
order of operations, do square root
first, as you would an exponent.
9. 10,00
0
5100
3
5(10) 3
50 3
47
Complete to evaluate each expression.
10. 3144
20
3
11. 25
144
13
20
13
20
13
12.
1
100
2
25
100
1
2
25
1
5
2
1
2
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Holt Mathematics
Name
Date
Class
Review for Mastery
LESSON
4E
Squares and Square Roots (continued)
Recall that the formula for the area of a
square is A s 2. A power in which the
exponent is 2 is called a square.
s2
s
s
Use the model to help you find the square.
13. 52
14. 92
5
9
9
5
A s2
A
A
A s2
2
•
A
A(
)2
A
•
A
Find the square.
15. 132
16. 162
17. 112
18. 72
The numbers 36 and 81 are perfect squares. Perfect squares are
numbers that are the squares of whole numbers.
The square root of 36 is 6. 36
6 because 6 • 6 36.
A table of square roots can help you estimate the square root of a
number that is not a perfect square.
Square Root
1
2
3
4
5
6
7
8
9
10
Perfect Squares
1
4
9
16
25
36
49
64
81
100
19. 44
20. 87
Find the perfect square nearest 44.
Find the perfect square nearest 87.
44 is closest to
87 is closest to
Since 49
44
is closest to
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.
Since 81
,
.
,
87
is closest to
.
117
Holt Mathematics
Name
LESSON
4E
Date
Class
Homework and Practice
Squares and Square Roots
Find the two square roots for each number.
1. 16
2. 9
3. 64
4. 121
5. 36
6. 100
7. 225
8. 400
Evaluate each expression.
9. 2
7
7
3
10. 4
1
9
5
11. 1
2
2
1
4
12. 1
6
7
3
2
13. 38
1
9
1
14. 252
5
15. 1
6
9
3
6
16. 1
9
6
25
8
1
17. 9
18. 4.96
4
2
2
5
19. 1
0
0
20. 2.5
2
5
21. Find the product of six and the sum of the square roots of 100
and 225.
22. Find the difference between the square root of 361 and the
square root of 289.
23. If a replica of the ancient pyramids were built with a base area
of 1,024 in.2, what would be the length of each side?( Hint: s A
)
24. The maximum displacement speed of a boat is found using the formula:
Maximum Speed in km/h 4.5 th
e
a
wte
rl
in
e
e
ln
g
th
f
oth
e
o
ba
tin
e
mte
rs
.
Find the maximum displacement speed of a boat that has a waterline
length of 9 meters.
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Holt Mathematics
Name
LESSON
4E
Date
Class
Homework and Practice
Squares and Square Roots, continued
Model each power using a square. Then evaluate the power.
25. 72
26. (2.6)2
27. (5.8)2
28. 262
29. 212
30. (1.7)2
31. (9.9)2
32. 132
Estimate each square root to the nearest whole number. Use a
calculator to check the reasonableness of your answers.
33. 3
3
34. 1
5
35. 8
1
36. 3
7
37. 2
4
38. 5
1
39. 8
40. 1
4
8
41. 6
4
42. 1
0
2
43. 4
6
44. 1
7
1
45. 9
0
46. 1
9
47. 8
3
48. 1
2
5
49. 3
50. 2
2
0
51. 1
3
6
52. 2
2
53. 5
0
0
54. 5
5
55. 6
1
0
56. 9
0
0
57. The area of a square tetherball court is 260 ft2. What is the
approximate length of each side of the court? Find your answer
to the nearest foot.
58. The area of square watch face is 6 cm2. What is the
approximate length of each side of the watch face? Find your
answer to the nearest tenth of a centimeter.
59. Brian jogs one time around a square park with an area of 4 mi2.
How far does Brian jog?
60. Steve wants to make a curtain to cover a square window with an
area of 9 ft2. How long should each side of the curtain be?
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119
Holt Mathematics
Answer Key
Homework and Practice 4D
Review for Mastery 4E
1. 612
1. yes; 11 11
2. 0.0079
2. no
3. 48,700
3. yes; 20 20
4. 0.093
4. 9; 9
5. 8,060
5. 25; 25
6. 0.00057
6. 13; 13
7. 0.0000317
7. 12
8. 0.0900613
8. 80
9. 0.0000985
9. 100
10. 60,040,000
10. 16
11. 82,300
11. 26
1
12. 0.00000148
12. 22
13. 25
7
13. 1.08 10
14. 5.943 101
14. 81
15. 4.2 101
15. 169
16. 6.73 105
16. 256
17. 5.6 103
17. 121
18. 6.004 103
18. 49
19. 8.52 103
19. 49; 7; 7
20. 2.46315 107
20. 81; 9; 9
21. 8.945 104
22. 5.702 103
Homework and Practice 4E
23. 8.005 109
1. 4
24. 1.2805 104
2. 3
24
25. 5.98 10
3. 8
kg
4. 11
26. 0.000000000753
5. 6
Exploration 4E
6. 10
1. Check students’ work.
7. 15
2. 100; 102
8. 20
3. 144; 169; 196; 225; 256; 289; 324; 361;
400
9. 8
4. The first n odd positive integers have a
sum of n 2.
10. 10
5. 1 3 5 … + 41 43 484
12. 12
11. 9
13. 30
14. 20
15. 7
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Holt Mathematics
Answer Key
16. 39
54. 7
17. 1
55. 25
18. 39.2
56. 30
19. 3
57. 16 ft
20. 4
58. 2.4 cm
21. 150
59. 8 mi
22. 2
60. 3 ft
23. 32 in.
Exploration 4F
24. 13.5 km/h
1. 4, 9, 16, 25, 36, 49, 64, 81, 100; 144,
169, 196, 225, 256, 289, 324, 361, 400
25. 49
26. 6.76
2–7. Estimates may vary.
27. 33.64
2. 3.1; 3.2
28. 676
3. 4.5; 4.5
29. 441
4. 14.1; 14.1
30. 2.89
5. 17.2; 17.3
31. 98.01
6. 7.5; 7.5
32. 169
7. 11.3; 11.4
33. 6
8. Sample; use the square root of the
closest integer square.
34. 4
35. 9
Technology Lab 4F
Think and Discuss
36. 6
37. 5
1. No; it does not terminate or repeat.
38. 7
2. An approximation; the actual square root
can’t be written because the decimal
continues forever.
39. 3
40. 12
41. 8
Try This
42. 10
1. 3.5 cm
43. 7
2. about 6.77 cm
44. 13
Review for Mastery 4F
45. 9
1. 36 39 49; 36
39
49
;
6 39
7
46. 4
47. 9
130
2. 121 130 144; 121
144
; 11 130
12
48. 11
106
121
; 10 106
3. 100
11; 6; 15; 100; 121
49. 2
50. 15
250
4. 225 250 256; 225
256
; 15 256
16; 225; 25; 256;
6; 16; 15
51. 12
52. 5
53. 22
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Holt Mathematics