MSM07G8_RESBK_Ch04_043-050.pe
1/29/06
12:14 PM
Page 46
Name
Date
Class
Reteach
LESSON
4-6 Estimating Square Roots
To locate a square root between two integers, refer to the table.
Number
1
2
3
4
5
6
7
8
9
10
Square
1
4
9
16
25
36
49
64
81
100
Number
11
12
13
14
15
16
17
18
19
20
121
144
169
196
225
256
289
324
361
400
Square
between two integers.
Locate 260
260 is between the perfect squares 256 and 289:
So:
And:
256 ⬍ 260 ⬍ 289
256
⬍ 260
⬍ 289
16
⬍ 260
⬍ 17
Use the table to complete the statements.
1.
36
⬍ 39
⬍
49
2.
36
⬍ 39
⬍
49
6
⬍ 39
⬍
7
121
121
11
⬍ 130
⬍
⬍ 130
⬍
⬍ 130
⬍
144
144
12
After locating a square root between two integers, you can
determine which of the two integers the square root is closer to.
27 is between the perfect squares 25 and 36:
25 ⬍ 27 ⬍ 36
So: 25
⬍ 27
⬍ 36
And: 5
⬍ 27
⬍6
The difference between 27 and 25 is 2;
25 ⬍ 27 ⬍ 36
the difference between 36 and 27 is 9.
2
9
So, 27
, is closer to 5.
Complete the statements.
4. 100
⬍ 106
⬍ 121
5.
225
⬍ 250
⬍
256
100
⬍ 106
⬍
121
225
⬍ 250
⬍
256
10
⬍ 106
⬍
11
15
⬍ 250
⬍
16
106 100 6
121 106 15
106
is closer to
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
250 256
10
than
11
225
250 250
is closer to
46
25
6
16
than
15
Holt Mathematics
MSM07G8_RESBK_Ch04_68-84.pe
1/30/06
11:49 AM
Page 78
Practice B
4-6 Estimating Square Roots
Practice A
4-6 Estimating Square Roots
LESSON
LESSON
Each square root is between two integers. Name the integers.
Explain your answer.
1. 10
Each square root is between two integers. Name the integers.
Explain your answer.
2. 8
3 and 4; 10 is between 9 and 16
1. 6
2 and 3; 8 is between 4 and 9
3. 19
2 and 3; 6 is between 4 and 9
4. 33
4 and 5; 19 is between 16 and 25
6 and 7; 39 is between 36 and 49
8. 18
3.5
11. 38
9. 7
2.6
12. 45
6.2
15. 54
2.8
7 and 8; 52 is between 49 and 64
8. 42
9. 21
10. 47
3.7
6.5
11. 58
4.6
12. 60
6.9
13. 35
14. 75
4.7
17. 40
5.2
7. 14
14. 22
6.7
7.3
5 and 6; 31 is between 25 and 36
4.9
13. 8
16. 27
6. 52
Use a calculator to find each value. Round to the nearest tenth.
10. 24
4.2
6 and 7; 44 is between 36 and 49
5. 31
Use a calculator to find each value. Round to the nearest tenth.
7. 12
4. 44
5 and 6; 28 is between 25 and 36
6. 39
3 and 4; 15 is between 9 and 16
4 and 5; 20 is between 16 and 25
3. 28
5 and 6; 33 is between 25 and 36
5. 15
2. 20
7.6
18. 48
6.3
7.7
5.9
8.7
Police use the formula r 25L
to approximate the rate of speed
in miles per hours of a vehicle from its skid marks, where L is the
length of the skid marks in feet.
6.9
The distance that a person can see from a certain height
to the horizon can be determined by using the formula
View 1.6
• h where the height is in feet and the
eight
result is in statute miles (defines miles between cities).
15. About how fast is a car going that leaves skid marks of 80 ft?
40 mi/h
16. About how fast is a car going that leaves skid marks of 245 ft?
19. How far to the horizon could you see if standing on top of Pike’s
Peak in Colorado, elevation 14,110 ft? Round the answer to the
nearest tenth.
70 mi/h
2
r
ᎏ,
17. If the formula for finding the length of the skid marks is L ᎏ20
what would be the length of the skid marks from a vehicle
traveling 80 mi/h?
150.3 statute miles
20. How far to the horizon could you see if flying in a plane at an
altitude of 30,000 ft? Round the answer to the nearest tenth.
320 ft
219.1 statute miles
43
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
LESSON
To locate a square root between two integers, refer to the table.
Each square root is between two integers. Name the integers.
Explain your answer.
1. 75
2. 104
8 and 9; 75 is between 64 and 81
10 and 11; 104 is between 100 and 121
3. 180
7. C: 0.36
D
1
1.2
1.4 1.6
11.87
10. 195
11. 0.024
5
39.19
17. 112
• 38
65.24
14. 53
• 38
15. 35
• (16
)
44.88
6.91
16. 25
• 28
23.66
18. 77
• 142
26.46
19. 66
• (98
) 20. 81
• (217
)
104.57
7
8
9
10
36
49
64
81
100
11
12
13
14
15
16
17
18
19
20
121
144
169
196
225
256
289
324
361
400
256 ⬍ 260 ⬍ 289
256
⬍ 260
⬍ 289
16
⬍ 260
⬍ 17
36
80.42
⬍ 39
⬍
49
2.
⬍ 39
⬍
121
⬍ 130
⬍
144
121
⬍ 130
⬍ 144
7
11
⬍ 130
⬍
12
After locating a square root between two integers, you can
determine which of the two integers the square root is closer to.
27 is between the perfect squares 25 and 36:
25 ⬍ 27 ⬍ 36
So: 25
⬍ 27
⬍ 36
And: 5
⬍ 27
⬍6
The difference between 27 and 25 is 2;
25 ⬍ 27 ⬍ 36
the difference between 36 and 27 is 9.
2
9
So, 27
, is closer to 5.
Find each product to the nearest hundredth.
• 24
13. 64
6
25
6
12. 47.7
0.16
13.96
5
16
36
⬍ 39
⬍ 49
Use guess and check to estimate each square root to the
nearest hundredth.
9. 141
4
9
Use the table to complete the statements.
A
1.
0.2 0.4 0.6 0.8
3
4
8. D: 0.09
C
0
2
1
between two integers.
Locate 260
260 is between the perfect squares 256 and 289:
So:
And:
13 and 14; 180 is between 169 and 196 15 and 16; 230 is between 225 and 256
B
1
Square
Square
Use a calculator to find each value. Round to the nearest tenth.
Use the indicated letter to graph each point on the number line.
6. B: 2.56
Number
Number
4. 230
1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
Holt Mathematics
Reteach
4-6 Estimating Square Roots
Practice C
4-6 Estimating Square Roots
LESSON
5. A: 1.21
44
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Complete the statements.
4. 100
132.58
⬍ 106
⬍ 121
5.
100
⬍ 106
⬍ 121
21. If the distance in feet traveled by a falling object is determined by
the formula d 16t 2, in which t is the time in seconds, find the
distance a falling object traveled in 22 sec.
10
7744 ft
22. If the distance traveled by the falling object was 3600 ft, how many
seconds did it take to fall?
⬍ 106
⬍
106 100 6
121 106 15
106
is closer to
225 ⬍ 250
11
15
250 than
256
11
16
⬍ 250
⬍
225 256 250 10
⬍
225
⬍ 250
⬍ 256
250
is closer to
25
6
16
than
15
15 sec
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
45
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
78
46
Holt Mathematics
Holt Mathematics