Free Printable Rational vs Irrational Numbers

1.

What is a rational number ?

a)

A rational number is a number that cannot be written as a fraction.

b)

A rational number is a number that can be written as a ratio.

c)

A rational number cannot be a repeating decimal.

2.

Irrational Numbers....

a)

cannot be represented as a simple fraction

b)

can be represented as a fraction

c)

can be a repeating decimal

3.

What type of number is π ?

a)

Rational

b)

Irrational

4.

Which number is irrational?

a)

9.6

b)

√45

c)

3/8

d)

3.4 x 10 ⁵

5.

Which number is a rational number ?

a)

1/4

b)

π

c)

√3

d)

∛25

6.

Which number is an irrational number?

a)

2.5

b)

5.72314.....

c)

-17

d)

1/2

7.

Which of the following numbers is rational?

a)

√8

b)

√16

c)

√50

d)

√75

8.

Which of the following is a rational number?

a)

π

b)

√8

c)

.56565656....

d)

√10

9.

Classify $\frac{\pi}{2}$

a)

Rational

b)

Irrational

10.

Classify $\frac{3}{5}$

a)

Rational

b)

Irrational

11.

Classify $\sqrt{5}$

a)

Rational

b)

Irrational

12.

Classify $\sqrt{121}$

a)

Rational

b)

Irrational

13.

$\sqrt{4}+\sqrt{4}=$

Solve:

a)

$4;\ rational$

b)

$\sqrt{8};\ irrational$

c)

$\sqrt{16};\ rational$

d)

$2\sqrt{4};\ irrational$

14.

Determine if the following number is a rational or irrational number.
$7.11$

a)

Rational

b)

Irrational

15.

$\sqrt{20}$

Determine if the number is a rational or irrational number.

a)

Rational

b)

Irrational

16.

$0.\overline{12}$

Determine if the number is a rational or irrational number.

a)

Rational

b)

Irrational

17.

$4\pi$

Determine if the number is a rational or irrational number.

a)

Rational

b)

Irrational

18.

$-8$

Determine if the number is a rational or irrational number.

a)

Rational

b)

Irrational

19.

$1.25$

Determine if the number is a rational or irrational number.

a)

Rational

b)

Irrational

20.

$\frac{1}{2}$

Determine if the number is a rational or irrational number.

a)

Rational

b)

Irrational

21.

$0.1294782374...$

Determine if the number is a rational or irrational number.

a)

Rational

b)

Irrational

22.

$\sqrt{50}$

Determine if the number is a rational or irrational number.

a)

Rational

b)

Irrational

23.

Complete the following statement explaining which two numbers are rational.

The two rational numbers are (a) because they (b) be expressed as a ratio of two integers.

Choose from the below words

$0\overline{.23}\ and\ \sqrt[]{49}$

can

cannot

$0.23\ and\ \sqrt[]{8}$

$\sqrt[]{8}and\ \sqrt[]{49}$

$\pi\ and\ \sqrt[]{49}$

$\pi\ and\ 0.\overline{23}$

24.

What numbers would be considered irrational?

a)

$0.3432032...$

b)

$-3.4$

c)

$\sqrt{15}$

d)

$\sqrt{25}$

25.

The √20 is between which two integers?

a)

2 & 3

b)

3 & 4

c)

4 & 5

d)

5 & 6

26.

The √40 is between which two consecutive whole numbers?

a)

7 & 8

b)

4 & 5

c)

5 & 6

d)

6 & 7

27.

Estimate the square root.

a)

4

b)

5

c)

6

d)

7

28.

Between which two whole numbers is the
√5?

a)

1 and 2

b)

2 and 3

c)

3 and 4

d)

4 and 5

29.

Estimate √119 to the nearest integer

a)

11

b)

12

c)

13

d)

10

30.

$\sqrt[3]{64}$

31.

Square roots are the opposite of ____________.

a)

Cube Roots

b)

Squaring

c)

Multiplication

d)

Absolute Value

32.

If I know the area of a square, how do I find the side length?

a)

I square the area.

b)

I divide the area by 2.

c)

I take the square root of the area.

d)

I divide the area by 4.

33.

What is the side length of a square that has an area of 36?

a)

9

b)

18

c)

6

d)

1296

34.

True or False. 49 a perfect square.

a)

True

b)

False

35.

1- Which number is a perfect square?

a)

a) 32

b)

b) 25

c)

c) 22

d)

D) 24

36.

Write √81 as and exponential expression.

a)

9³

b)

9¹

c)

9²

d)

8²

37.

2⁵ is the same as 2 x 5.

a)

True

b)

False

38.

Which of the following is a perfect square?

a)

39

b)

6

c)

50

d)

81

39.

In what category does $\frac{6}{11}$ belong ?

a)

Integer

b)

Natural Number

c)

Rational Number

40.

A repeating decimal is what type of number?

a)

Rational

b)

Irrational

41.

What is the square root 64?

a)

8

b)

-8

c)

8 and -8

d)

18

42.

$-\sqrt[]{49}$

a)

7

b)

-7

c)

-7,7

d)

8

43.

What type of answers do square roots have

a)

positive

b)

negative

c)

positive and negative

d)

none

44.

Simplify $\sqrt[]{\frac{16}{64}}$

a)

only 1/2

b)

only -1/2

c)

both 1/2 and -1/2

45.

Simplify $\sqrt[]{169}$ .

(a)

46.

∛216

a)

6

b)

72

c)

108

d)

4

47.

Evaluate ∛1

a)

1

b)

2

c)

3

d)

4

48.

What number, n, cubed is equal to 64?

n³ = 64

a)

4

b)

2

c)

8

d)

262,144

49.

$\sqrt{\left(\frac{16}{81}\right)}\ \ =\ ?$

a)

$\frac{8}{27}$

b)

$\frac{8}{9}$

c)

$\frac{4}{9}$

d)

$\frac{4}{3}$

50.

Solve.

$\sqrt{-96}$

a)

9.79

b)

9.8

c)

Not possible

d)

-9.8

51.

Solve.

$-\sqrt{144}$

a)

12

b)

-12

c)

-72

d)

Not possible

52.

Cubing a number means multiplying a number by itself 3 times.

a)

True

b)

False

53.

The inverse operation for SQUARING a number is finding the CUBE root?

a)

true

b)

false

54.

Cube root of positive number

a)

Positive

b)

Negative

c)

Can't say

55.

Cube root of negative number

a)

Positive

b)

Negative

c)

Can't say

56.

Symbol for "cube root"

a)

∛

b)

$\sqrt{ }$

c)

$\angle$

d)

$\sum_{ }^{ }$

57.

x³=-27

a)

x=3

b)

x=27

c)

x=-3

d)

x=54

58.

Find the side length of a cube with a volume of $512cm^3$

a)

6 cm

b)

7 cm

c)

8 cm

Rational vs Irrational Numbers

Total questions: 58

Worksheet time: 2hrs 40mins

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