Free Printable Practice of Real Number System

1.

Put in the symbol to make the statement true...
-17.5 _________ -√121

a)

>

b)

<

c)

=

2.

Which number has a greater value?

a)

√2

b)

⁵/₄

3.

True or False?

$\frac{7}{8}>\frac{\sqrt[]{9}}{4}$

a)

True

b)

False

4.

Change 4% to a decimal.

a)

.04

b)

.004

c)

.4

d)

4

5.

a)

A, B, C

b)

B, C, A

c)

C, A, B

d)

A, C, B

6.

Which point most closely corresponds to the √8 on the number line below? (Click the question to see the picture)

a)

P

b)

Q

c)

R

d)

S

7.

Look at the number line.
Which point on the number line best represents √12 ?

a)

D

b)

E

c)

F

d)

G

8.

List the following numbers from least to greatest:
-64 , 3.5 , √27 , 6.666...

a)

-64 , 3.5 , √27 , 6.666...

b)

3.5 , √27 , 6.666..., -64

c)

3.5, -64, √27, 6.666...

d)

6.666, √27, -64, 3.5

9.

Which of these values is the GREATEST?

a)

63/7

b)

8.99

c)

450%

d)

-22

10.

Which set is in descending order?

a)

15% .45 9/10

b)

.45 15% 9/10

c)

9/10 15% .45

d)

9/10 .45 15%

11.

List in order from least to greatest.
5/4, 56%, 1.07, 4/5

a)

^{5/4, 56%, 1.07, 4/5}

b)

^{1.07, 4/5, 5/4, 56%}

c)

^{56%, 1.07, 4/5, 5/4}

d)

^{56%, 4/5, 1.07, 5/4}

12.

Which is ordered least to greatest?

a)

1/4, -3/7, 1/2

b)

-3/7, 1/2, 1/4

c)

1/2, 1/4, -3/7

d)

-3/7, 1/4, 1/2

13.

Order 3π , √10 , and 3.25 from greatest to least.

a)

√ 10, 3π, 3.25

b)

√ 10, 3.25, 3π

c)

3π, 3.25, √ 10

d)

3.25, √ 10, 3π

14.

What is 37% as a decimal?

a)

37

b)

.37

c)

3.7

d)

.037

15.

Express 32 1/2 in decimal form.

a)

32.4

b)

32.5

c)

32.75

d)

32.25

16.

What is the decimal equivalent of 3/5?

a)

0.3

b)

3.5

c)

0.6

d)

0.2

17.

Which set is in descending order?

a)

15% .45 9/10

b)

.45 15% 9/10

c)

9/10 15% .45

d)

9/10 .45 15%

18.

Put in the symbol to make the statement true...
-17.5 _________ -√121

a)

>

b)

<

c)

=

19.

Choose the categories that apply to the value

\sqrt{\frac{16}{4}}

a)

natural number

b)

whole number

c)

integer

d)

rational number

e)

irrational number

20.

Choose the categories that apply to -7.5.

a)

natural number

b)

whole number

c)

integer

d)

rational number

e)

real number

21.

5.4545454545454545... is a

a)

natural number

b)

whole number

c)

integer

d)

rational number

e)

real number

22.

The number 0 is a

a)

natural number

b)

whole number

c)

integer

d)

rational number

e)

irrational number

23.

The value $-\sqrt{121}$ is a(n)

a)

natural number

b)

whole number

c)

integer

d)

rational number

e)

irrational number

24.

The value -18/6 is a(n)

a)

natural number

b)

whole number

c)

integer

d)

rational number

e)

irrational number

25.

Chose the most specific group to classify the numbers below.

{... -3, -2, -1, 0, 1, 2, 3...}

a)

Rational Numbers

b)

Whole Numbers

c)

Natural Numbers

d)

Integers

26.

Chose the most specific group to classify the numbers below.

{ 0, 1, 2, 3, 4, ...}

a)

Real Numbers

b)

Integers

c)

Whole Numbers

d)

Natural Numbers

27.

Chose the most specific group to classify the numbers below.

$\sqrt{2}$ , $\pi$ , 7.123875438345973...

a)

Rational Numbers

b)

Irrational Numbers

c)

Real Numbers

d)

Integers

28.

Chose the most specific group to classify the numbers below.

$-\sqrt{9}$ , $\frac{14}{2}$ , $\frac{-3}{\ \ \ 3}$ , $\sqrt{49}$

a)

Integers

b)

Irrational Numbers

c)

Natural Numbers

d)

Whole numbers

29.

Classify the real number by checking all that apply!
$-6.75$

a)

Natural

b)

Whole

c)

Integer

d)

Rational

e)

Irrational

30.

Classify the real number by checking all that apply!
$\sqrt{175}$

a)

Natural

b)

Whole

c)

Integer

d)

Rational

e)

Irrational

31.

Classify the real number by checking all that apply!

$\frac{30}{3}$

a)

Natural

b)

Whole

c)

Integer

d)

Rational

e)

Irrational

32.

Classify the real number by checking all that apply!
$-\sqrt{9}$

a)

Natural

b)

Whole

c)

Integer

d)

Rational

e)

Irrational

33.

$\frac{3}{4}$

Classify the following number

(select all that apply)

a)

Whole

b)

Integer

c)

Rational

d)

Real

e)

Irrational

34.

Classify the following number (select all that apply)

-24.290835710239483...

a)

Whole

b)

Integer

c)

Rational

d)

Real

e)

Irrational

35.

Classify the following number (select all that apply)

-24.33333333333...

a)

Whole

b)

Integer

c)

Rational

d)

Real

e)

Irrational

36.

Classify the following number (select all that apply)

-24.3

a)

Whole

b)

Integer

c)

Rational

d)

Real

e)

Irrational

37.

Classify the following number (select all that apply)

-24

a)

Whole

b)

Integer

c)

Rational

d)

Real

e)

Irrational

38.

Classify the following number (select all that apply)

24

a)

Whole

b)

Integer

c)

Rational

d)

Real

e)

Irrational

39.

Identify each irrational number.

a)

$\sqrt{50}$

b)

$-4\frac{2}{7}$

c)

$-\sqrt{400}$

d)

$34.145$

e)

$7.745966692...$

40.

Identify each rational number.

a)

$\sqrt{121}$

b)

$\frac{3}{11}$

c)

$\sqrt{-36}$

d)

$0$

e)

$4.123105626...$

41.

Classify this number: √25

a)

real

b)

real rational

c)

real rational integer

d)

real rational integer whole

42.

Classify this number: -12

a)

real

b)

real rational

c)

real irrational

d)

real rational integer

43.

Classify this number: ⅚

a)

real

b)

real rational

c)

real rational integer

d)

real rational integer whole

44.

Evaluate $\sqrt[]{0}$

(a)

45.

Evaluate $\sqrt[]{0}$

(a)

46.

Evaluate $\sqrt[]{1}$

(a)

47.

Evaluate $\sqrt[]{4}$

(a)

48.

Evaluate $\sqrt[]{9}$

(a)

49.

Evaluate $\sqrt[]{16}$

(a)

50.

Evaluate $\sqrt[]{25}$

(a)

51.

Evaluate $\sqrt[]{36}$

(a)

52.

Evaluate $\sqrt[]{49}$

(a)

53.

Evaluate $\sqrt[]{64}$

(a)

54.

Evaluate $\sqrt[]{81}$

(a)

55.

Evaluate $\sqrt[]{100}$

(a)

56.

Evaluate $\sqrt[]{121}$

(a)

57.

Evaluate $\sqrt[]{144}$

(a)

58.

Evaluate $\sqrt[3]{8}$

(a)

59.

Evaluate $\sqrt[3]{27}$

(a)

60.

Evaluate $\sqrt[3]{64}$

(a)

61.

Evaluate $\sqrt[3]{125}$

(a)

62.

What does this symbol represent?

a)

square root

b)

divide by 2

c)

cube root

d)

greater than or less than

63.

$9^2=18$ True or false?

a)

True

b)

False

64.

Evaluate: $\sqrt{81}$ Select the TWO answers that apply

a)

9

b)

8

c)

-9

d)

-8

65.

$\sqrt{\frac{64}{25}}=\frac{y}{5}$
What is y?

a)

4

b)

8

66.

Evaluate: $\sqrt{-25}$

a)

$5$

b)

$-5$

c)

$\left(-5\right)^2$

d)

Can't be solved

67.

x² = 121
What does x equal?

a)

11²

b)

11 and -11

c)

20 and 11

d)

12 and 1

68.

Solve the following equation for x: $x^2=\frac{1}{64}$

Select the TWO answers that apply

a)

$-\frac{1}{4}$

b)

$\frac{1}{4}$

c)

$-\frac{1}{8}$

d)

$\frac{1}{8}$

69.

A square poster has an area of 81 square inches. What is the length of each side of the square?

a)

3 inches

b)

9 inches

c)

20.25 inches

d)

40.5 inches

70.

Evaluate. 8³

a)

512

b)

398

c)

43

d)

764

71.

$\left(\frac{2}{3}\right)^3=$

a)

4/9

b)

2/3

c)

6/9

d)

8/27

72.

Solve each equation for x:

a)

4

b)

4 and -4

c)

16 and -16

d)

16

73.

What is the cube root of 27?

a)

9

b)

3

c)

-3

d)

-9

74.

What is the cube root of 125?

a)

5

b)

-5

c)

25

d)

-25

75.

$^3\sqrt{-8}$ =

a)

2

b)

-2

c)

±2

d)

None

76.

$^3\sqrt{216}=$

a)

5

b)

6

c)

7

d)

8

77.

$^3\sqrt{-64}=$

a)

-8

b)

8

c)

-4

d)

4

78.

Solve the following equation for x: $x^3=\frac{1}{64}$

a)

$-\frac{1}{8}$

b)

$\frac{1}{8}$

c)

$\frac{1}{4}$

d)

$-\frac{1}{4}$

79.

The volume of a cube is 1,000 cm³. What is the length of each side of the cube?

a)

1

b)

10

c)

100

d)

300

80.

Ms. Cummings is hanging a square picture frame that has an area of 169 cm². Find the side length of the frame.

a)

12 cm

b)

13 cm

c)

13 in

d)

16 cm

81.

Ms. Cummings is hanging a square picture frame that has an area of $169\ cm^2$ . Determine the perimeter of the frame.

(a)

82.

Which of the following is the best approximation of $\sqrt{167}$ ?

a)

12.9

b)

12.3

c)

12

d)

13

83.

Which of the following is the best approximation of $\sqrt{220}$ ?

a)

14.8

b)

14.3

c)

14

d)

15

84.

Which of the following is the best approximation of $\sqrt{200}$ ?

a)

14.1

b)

14.7

c)

14

d)

15

85.

Which of the following is the best approximation of $\sqrt{167}$ ?

a)

12.9

b)

12.3

c)

12

d)

13

86.

Which of the following is the best approximation of $\sqrt{220}$ ?

a)

14.8

b)

14.3

c)

14

d)

15

87.

Which of the following is the best approximation of $\sqrt{200}$ ?

a)

14.1

b)

14.7

c)

14

d)

15

88.

Which of the following is the best approximation of $\sqrt{175}$ ?

a)

13.2

b)

13.7

c)

14

d)

13

89.

Which of the following is the best approximation of $\sqrt{125}$ ?

a)

11.2

b)

11.8

c)

12

d)

11

90.

Which of the following is the best approximation of $\sqrt{107}$ ?

a)

10.3

b)

10.8

c)

10

d)

11

91.

Which of the following is the best approximation of $\sqrt{96}$ ?

a)

9.4

b)

9.8

c)

10

d)

9

92.

Which of the following is the best approximation of $\sqrt{70}$ ?

a)

8.4

b)

8.7

c)

8

d)

9

93.

Which of the following is the best approximation of $\sqrt{54}$ ?

a)

7.3

b)

7.8

c)

8

d)

7

94.

Which of the following is the best approximation of $\sqrt{45}$ ?

a)

6.7

b)

6.2

c)

6

d)

7

95.

Which of the following is the best approximation of $\sqrt{27}$ ?

a)

5.2

b)

5.7

c)

6

d)

5

96.

Which of the following is the best approximation of $\sqrt{22}$ ?

a)

4.7

b)

4.4

c)

4

d)

5

97.

Which of the following is the best approximation of $\sqrt{10}$ ?

a)

3.2

b)

3.6

c)

4

d)

3

98.

Which of the following is the best approximation of $\sqrt{8}$ ?

a)

2.8

b)

2.2

c)

2

d)

3

99.

Which of the following is the best approximation of $\sqrt{2}$ ?

a)

1.4

b)

1.8

c)

2

d)

1

100.

Which of the following is the best approximation of $\sqrt{225}$ ?

a)

14.8

b)

14.3

c)

14

d)

15

101.

Which of the following is the best approximation of $\sqrt{196}$ ?

a)

14.1

b)

14.7

c)

14

d)

15

102.

Which of the following is the best approximation of $\sqrt{169}$ ?

a)

13.2

b)

13.7

c)

14

d)

13

103.

Which of the following is the best approximation of $\sqrt{144}$ ?

a)

11.2

b)

11.8

c)

12

d)

11

104.

Which of the following is the best approximation of $\sqrt{121}$ ?

a)

11.2

b)

11.8

c)

12

d)

11

105.

Between which two integers is the square root of 20?

a)

2 & 3

b)

3 & 4

c)

4 & 5

d)

5 & 6

106.

Between what two integers is the square root of 44?

a)

3 and 4

b)

4 and 5

c)

5 and 6

d)

6 and 7

107.

Compare using >, < or =. Show all your work! $\sqrt{225}$ _______ $\sqrt[3]{1728}$

a)

$\sqrt{225} = 15$ and $\sqrt[3]{1728} = 12$ therefore $\sqrt{225} > \sqrt[3]{1728}$

b)

$\sqrt{225} = 15$ and $\sqrt[3]{1728} = 15$ therefore $\sqrt{225} = \sqrt[3]{1728}$

c)

$\sqrt{225} = 14$ and $\sqrt[3]{1728} = 15$ therefore $\sqrt{225} < \sqrt[3]{1728}$

d)

$\sqrt{225} = 15$ and $\sqrt[3]{1728} = 16$ therefore $\sqrt{225} < \sqrt[3]{1728}$

108.

Compare using >, < or =. Show all your work! 3.1 _______ $\sqrt{12}$

a)

3.1 > $\sqrt{12}$

b)

3.1 $\sqrt{12}$

c)

3.1 = $\sqrt{12}$

d)

3.1 \neq $\sqrt{12}$

109.

a)

A

b)

B

c)

C

d)

D

110.

a)

A

b)

B

c)

C

d)

D

111.

a)

9

b)

10

112.

a)

a

b)

b

c)

c

d)

d

113.

A cube has a volume of 125 cm³. What is the length of each side of the cube?

a)

5 cm

b)

25 cm

c)

15 cm

114.

In between what two integers is the square root of 77?

a)

5 and 6

b)

6 and 7

c)

7 and 8

d)

8 and 9

115.

Estimate the square root.

a)

9

b)

9 6/19

c)

9 3/17

d)

10

116.

Estimate the square root.

a)

5

b)

5 4/11

c)

5 1/2

d)

6

117.

Solve

x^3=125

a)

-5

b)

5

c)

4

d)

25

118.

Solve for p when p² = 100.

a)

1,000, -1,000

b)

10, -10

c)

0.10

d)

-0.10

119.

6³ = ?

a)

196

b)

206

c)

216

d)

226

120.

$^3\sqrt{8}=$

a)

2

b)

-2

c)

±2

d)

None

121.

Which two consecutive numbers is ∛30 in between

a)

3 and 4

b)

5 and 6

c)

7 and 8

d)

9 and 10

122.

Which two consecutive numbers is ∛12 in between

a)

3 and 4

b)

7 and 8

c)

2 and 3

d)

5 and 6

123.

Which two consecutive numbers is ∛192 in between

a)

9 and 10

b)

5 and 6

c)

7 and 8

d)

11 and 12

124.

Which two consecutive numbers is ∛300 in between

a)

8 and 9

b)

9 and 10

c)

7 and 8

d)

6 and 7

125.

Which two consecutive numbers is ∛590 in between

a)

13 and 14

b)

7 and 8

c)

8 and 9

d)

14 and 15

126.

Which number is an estimate to ∛186

a)

5.8

b)

5.5

c)

5.7

d)

5.1

127.

Which number is an estimate to ∛58

a)

4.2

b)

4.1

c)

3.8

d)

3.9

128.

Which number is an estimate to ∛10

a)

2.3

b)

2.0

c)

2.1

d)

2.2

129.

Which number is an estimate to ∛163

a)

5.7

b)

5.9

c)

5.6

d)

5.5

130.

Which number is an estimate to ∛799

a)

9.2

b)

9.3

c)

8.9

d)

9.5

131.

Which number is the closest to ∛131

a)

⁵

b)

6

c)

4

d)

7

132.

Which cube root is the closest to ∛287

a)

6

b)

7

c)

5

d)

9

133.

Which number is the closest to ∛569

a)

10

b)

9

c)

8

d)

7

134.

Which number is the closest to ∛610

a)

8

b)

9

c)

10

d)

11

135.

Which number is the closest to ∛33

a)

3

b)

4

c)

6

d)

7

136.

Between which two whole numbers is this located?
√110

a)

5 and 6

b)

7 and 8

c)

10 and 11

d)

11 and 12

137.

Between which two whole numbers is this located?
√55

a)

2 and 3

b)

7 and 8

c)

8 and 9

d)

4 and 5

Practice of Real Number System

Total questions: 137

Worksheet time: 9hrs 6mins

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