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Date
Class
Practice B
LESSON
3-10 The Real Numbers
Write all names that apply to each number.
7
ᎏ
冪ᎏ莦
2
18
1. ⴚ ᎏ8ᎏ
2. 兹0.15
苶
3.
4. 兹45
苶
5. ⴚ25
6. ⴚ6.75
State if the number is rational, irrational, or not a real number.
苶
7. 兹14
8. 兹ⴚ16
苶
7
11. ᎏ2ᎏ
0
12. ⴚ兹81
苶
6.2
9. ᎏ0ᎏ
10. 兹49
苶
冪ᎏ莦9ᎏ
14. ⴚ1.3
13.
7
Find a real number between each pair of numbers.
3
4
15. 7ᎏ5ᎏ and 7ᎏ5ᎏ
13
16. 6.45 and ᎏ2ᎏ
7
9
ᎏ
17. ᎏ8ᎏ and ᎏ
10
18. Give an example of a rational number between ⴚ兹4
苶 and 兹4
苶
19. Give an example of an irrational number less than 0.
20. Give an example of a number that is not real.
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93
Holt Pre-Algebra
Holt Middle
School Math
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Practice B
LESSON
3-10 The Real Numbers
LESSON
3-10 The Real Numbers
Write all names that apply to each number.
Write all names that apply to each number.
2
2. ᎏ5ᎏ
1. ⴚ3.2
7
1. ⴚ ᎏ8ᎏ
3. ⴚ兹12
苶
rational; real
rational; real
2. 兹0.15
苶
rational; real
irrational; real
3.
ᎏᎏ
冪莦
2
irrational; real
18
whole; integer;
rational; real
兹4
苶
4. ᎏ
2
5. ⴚ20
4. 兹45
苶
6. 兹16
苶
irrational; real
whole; integer;
integer; rational;
whole; integer;
rational; real
real
rational; real
苶
8. 兹7
rational
irrational
苶
7. 兹14
3
11. ᎏ4ᎏ
not real
12. 兹25
苶
rational
rational
7
ᎏ
11. ᎏ
20
14. 兹11
苶
rational
1
2
1
2
7
50
sample answer: ᎏᎏ
sample answer: 2.18
4
rational
冪莦
7
ᎏᎏ
9
14. ⴚ1.3
irrational
13
rational
7
9
17. ᎏ8ᎏ and ᎏ1ᎏ
0
16. 6.45 and ᎏ2ᎏ
7
sample answer: 7ᎏᎏ
10
22
25
sample answer: ᎏᎏ
sample answer: 6.48
18. Give an example of a rational number between ⴚ兹4
苶 and 兹4
苶
sample answer: 0
sample answer: 兹5
苶
19. Give an example of an irrational number less than 0.
兹22
苶
sample answer: ⫺ ᎏ
7
sample answer: 兹⫺25
苶
1
20. Give an example of a rational number between ᎏ2ᎏ and 兹1
苶.
20. Give an example of a number that is not real.
3
4
2
0
sample answer: ᎏᎏ
sample answer: ᎏᎏ
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Middle
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Write all names that apply to each number.
兹17
苶
2. ᎏ
21
1. 0.318
苶
rational; real
not real
5. 兹6.15
苶
irrational;
real
real
Square roots of numbers that are
perfect squares are rational.
real
rational; real
12. C: 兹7
苶
1.5
2
C
B
1. 兹7
苶
2.5
3
4.5
rational
irrational
2
5
Tell if each number is real or not real.
5. ⴚ8
sample answer: 1.2
11
ᎏ and 1.
15. Find a real number between ᎏ
12
6. ⴚ兹8
苶
real
23
sample answer: ᎏ2ᎏ
4
7. 兹ⴚ8
苶
real
8. 兹ⴚ25
苶
not real
not real
Between any two real numbers, there is always another real number.
One way to find a number between is to find the number halfway
between.
16. Find a real number between ⴚ0.25 and ⴚ0.3.
sample answer: ⫺0.26
1
2
To find a real number between 7ᎏ5ᎏ and 7ᎏ5ᎏ,
1
2
3
3
divide their sum by 2: 7ᎏ5ᎏ ⴙ 7ᎏ5ᎏ ⴝ 14ᎏ5ᎏ ⴜ 2 ⴝ 7ᎏ1ᎏ
0
Find a real number between each pair. Possible answers
10
9
ᎏ and ᎏ ᎏ.
17. Find a real number between ᎏ
11
11
共 兲
41
sample answer: ᎏ5ᎏ
0
18. Find a real number between 兹28
苶 and 兹30
苶.
3
4
9. 8ᎏ7ᎏ and 8ᎏ7ᎏ
sample answer: 5.3
1
8ᎏ2ᎏ
Copyright © by Holt, Rinehart and Winston.
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rational
4. 兹101
苶
The square of a nonzero number is positive. 3 ⴝ 9 and (ⴚ3) ⴝ 9
So, the square root of a negative number is not a real number.
兹ⴚ9
苶 is not a real number.
13. D: 兹18
苶
4
3. 兹169
苶
2
D
3.5
2. 兹81
苶
irrational
14. Find a real number between 兹1
苶 and 兹2
苶.
94
兹3
苶 ⴝ 1.732050807. . .
Tell if each number is rational or irrational.
irrational; real
Use the indicated letter to approximate each irrational number
on the number line.
1
Square roots of numbers that are
not perfect squares are irrational.
兹25
苶ⴝ5
whole; integer;
0.5
Irrational Numbers
9. 兹112
苶
integer; rational;
A
Rational Numbers
Together, the rational numbers and the
irrational numbers form the set of real numbers.
rational; real
8. 兹64
苶 ⴙ 15
11. B: ␲
Real Numbers
Irrational numbers can only be written
as decimals that do not end or repeat.
21
ᎏ
6. ⴚ ᎏ22
integer; rational;
7. ⴚ兹196
苶
The set of rational numbers contains
all integers, all fractions, and
decimals that end or repeat.
3. 兹ⴚ100
苶
irrational; real
兹144
苶
4. ᎏ
ⴚ6
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Reteach
LESSON
3-10 The Real Numbers
Practice C
LESSON
3-10 The Real Numbers
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
13.
rational
15. 7ᎏ5ᎏ and 7ᎏ5ᎏ
19. Give an example of a number that is not real.
0
not real
12. ⴚ兹81
苶
3
1
1
17. ᎏ8ᎏ and ᎏ5ᎏ
18. Give an example of an irrational number that is greater than 0.
苶
10. A: 兹3
10. 兹49
苶
Find a real number between each pair of numbers.
11
16. 2.16 and ᎏ5ᎏ
sample answer: 3ᎏᎏ
not real
rational
irrational
Find a real number between each pair of numbers.
15. 3ᎏ3ᎏ and 3ᎏ3ᎏ
rational; real
6.2
9. ᎏ0ᎏ
8. 兹ⴚ16
苶
irrational
not real
13. ⴚ兹49
苶
integer; rational;
State if the number is rational, irrational, or not a real number.
兹9
苶
10. ᎏ
0
9. 兹ⴚ4
苶
6. ⴚ6.75
real
State if the number is rational, irrational, or not a real number.
7. 0
5. ⴚ25
Pre-Algebra
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Middle
School Math
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135
10. ⴚ1.6 and ⴚ1.7
7
2
are shown.
11. ⴚ3ᎏ9ᎏ and ⴚ3ᎏ9ᎏ
1
⫺3ᎏ2ᎏ
⫺1.65
95
1
3
12. 6ᎏ2ᎏ and 6ᎏ4ᎏ
5
6ᎏ8ᎏ
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