e x p l o r at i o n
Georgia Performance
Standards
4F
M8N1.f,
Estimating Square Roots M8N1.c,
M8N1.k
Knowing the square numbers can help you estimate
square roots.
1. Complete the table of squares.
12
22
32
42
52
62
72
82
92
102
122
132
142
152
162
172
182
192
202
1
112
121
Use the table of squares above to help you estimate each
square root to the nearest tenth. Use a calculator to check
your estimates. Round to two decimal places.
Square Root
2.
3.
4.
5.
6.
7.
Estimate
Calculator
10
20
200
300
57
130
Think and Discuss
8. Discuss your strategy for estimating square roots.
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Name
Date
LAB
Technology Lab
4F
Finding Square Roots
Class
If you know the area of a square or circle and need to find the
length of the side or the radius, you can find your answer by using
square roots.
Activity
The area of a square is 289 cm2. What is the length of a side?
s 289
On your graphing calculator use the following keystrokes to find the
square root:
2nd
x2
289
ENTER
The length of a side is 17 cm.
The area (A) of a circle is 520 cm2. What is the radius of the circle?
A
520
r 165.5
2
12.87
A r 2
On your calculator use the following keystrokes:
␲
2nd
x2
520
2nd
ENTER
The radius is about 12.87 cm.
Think and Discuss
1. Enter on your calculator. Is a rational number? Explain
why or why not.
2. Use your calculator to find the square root of pi. Is the number
you see in your display the actual square root or an approximate
square root? How do you know?
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Holt Mathematics
Name
Date
LAB
Technology Lab
4F
Finding Square Roots, continued
Class
Try This
1. Find the length (s) of a side of a square with an area A of 12.25
cm2. Show the buttons you pressed on your calculator to find
the answer.
2. Find the radius of a circle with an area of 144 cm2. Show the
buttons you pressed on your calculator to find the answer.
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Holt Mathematics
Name
LESSON
4F
Date
Class
Review for Mastery
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
11
12
13
14
15
16
17
18
19
20
121
144
169
196
225
256
289
324
361
400
Number
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.
39
1.
130
2.
39
130
39
130
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.
3. 100
106
121
250
4.
106
250
106
250
106 100 250 121 106 106
is closer to
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250 250
is closer to
than
123
than
Holt Mathematics
Name
LESSON
4F
Date
Class
Homework and Practice
Finding Square Roots
Each square root is between two integers. Name the integers.
1. 1
0
2. 2
4
3. 5
1
4. 3
9
5. 6
6
6. 3
0
7. 7
8
8. 8
7
Use a calculator to find each value. Round to the nearest tenth.
9. 1
8
10. 6
3
11. 1
9
12. 4
1
13. 5
3
14. 9
8
15. 5
4
16. 7
2
17. 8
3
18. 1
2
0
19. 2
0
0
20. 4
8
9
21. The distance a person can see at sea is measured in miles by using the
formula d 2 h, where h is the height in ft above sea level. About how many
3
miles can a person see that is 8 feet above sea level? Round the answer to the
nearest tenth of a mile.
22. The length of the hypotenuse of a right triangle is the square root of the sum of the
squares of the measures of the other two legs of the triangle. Approximate the
length of the hypotenuse of a right triangle if the legs have measures 12 and 15.
23. At an accident scene, a police officer may determine the rate of speed, r, in mi/h,
of the car by using the following formula r 2
0
, where is length of the skid
marks. How fast was a car going if the skid marks at the scene are 180 ft long?
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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
Answer Key
Homework and Practice 4F
Try This
Yes; segment AE has length 2s and segment
BE has length s5
.
1. 3 and 4
2. 4 and 5
Technology Lab 4G
Think and Discuss
3. 7 and 8
4. 6 and 7
1. Sample: the mixed fractions have a
fraction part and a whole number part.
5. 8 and 9
6. 5 and 6
Try This
7. 8 and 9
8. 9 and 10
1. 2
9. 4.2
2. 13
3. 2.5
2
10. 7.9
11. 4.4
4. 3
12. 6.4
Review for Mastery 4G
13. 7.3
14. 9.9
1. irrational
15. 7.3
2. rational
16. 8.5
3. rational
17. 9.1
4. irrational
18. 11.0
5. real
19. 14.1
6. real
20. 22.1
7. not real
21. 3.5 mi
8. not real
1
9. 82
10. –1.65
22. about 19.2
23. about 19.0 mi/h
5
11. –39
Exploration 4G
1. rational
5
2. irrational
12. 68
3. rational
Homework and Practice 4G
1. real, rational, integer, whole number,
natural number
4. rational
5. rational
6. The decimal representation of the
number repeats or terminates.
2. real, rational
7. The decimal representation of the
number does not repeat or terminate.
4. real, rational, integer
3. real, rational
5. real, rational
6. real
Hands-On Lab 4G
Think and Discuss
7. rational
1. (s2
)(s2
) 2s 2 and (s3
)(s3
) 3s 2
8. rational
2. No, rulers do not have units of 2
or 3
.
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