Free Printable Modeling with Rational & Irrational Numbers

1.

$\sqrt{64}$

a)

4

b)

6

c)

9

d)

8

2.

∛8 =

a)

4

b)

3

c)

2

d)

512

3.

∛216

a)

6

b)

72

c)

108

d)

4

4.

$-\sqrt{144}$

a)

12

b)

-12

c)

-72

d)

none of the above (imaginary number)

5.

$\sqrt{-144}$

a)

12

b)

-12

c)

72

d)

none of the above (imaginary number)

6.

$\sqrt[3]{-1}$ (cube root of -1)

a)

$\pm1$

b)

1

c)

-1

d)

none of the above (imaginary number)

7.

A cube with side length s has a volume of 64 cubic units. What is the length of one side?

a)

4

b)

8

c)

16

d)

32

8.

Select the set with all perfect squares.

a)

-144, 9, 50, 75, 81, 100

b)

9, 50, 81, 100

c)

9, 50, 75, 81, 100

d)

9, 81, 100

9.

Choose every value that is a perfect cube:

a)

27

b)

1,000

c)

90

d)

1

10.

Which number is both a perfect square and perfect cube?

a)

4

b)

64

c)

125

d)

8

11.

$-\sqrt{8}\times\sqrt{8}$

a)

-8

b)

$-\sqrt{16}$

c)

$\sqrt{-64}$

d)

$-\sqrt{64}$

12.

$\sqrt{18},\ 4.2,\ -\sqrt{16},\ \sqrt{16}$ List from least to greatest:

a)

$-\sqrt{16},\ \sqrt{16},\ 4.2,\ \sqrt{18}$

b)

$-\sqrt{16},\ \sqrt{16},\ \sqrt{18},\ 4.2$

c)

$-\sqrt{16}and\ \sqrt{16\ }\ are\ equal,\ 4.2,\ \sqrt{18}$

d)

$\sqrt{18},\ 4.2,\ \sqrt{16},\ -\sqrt{16}$

13.

$\sqrt{-4}$

a)

2i

b)

-2i

c)

2

d)

4i

14.

A room is a square with an area of 900 square feet. What is the perimeter around the edge of the room?

a)

900 feet

b)

60 feet

c)

120 feet

d)

30 feet

15.

Which is equivalent to ∛54 in simplest form?

a)

3∛6

b)

9∛2

c)

3∛2

d)

3∛3

16.

Which is equivalent to ∛375 in simplest form?

a)

3∛5

b)

5∛25

c)

3∛125

d)

5∛3

17.

Simplify.

a)

A

b)

B

c)

C

d)

D

18.

Simplify.

a)

A

b)

B

c)

C

d)

D

19.

∛32

a)

4∛2

b)

2∛4

c)

2

d)

Simplified

20.

Simplify:
√96

a)

4√6

b)

3√6

c)

6√5

d)

6√8

21.

Simplify:
√24

a)

2√6

b)

4√6

c)

2√12

d)

3√8

22.

∛81

a)

Simplified

b)

3∛3

c)

9

d)

27∛3

23.

√108

a)

3√12

b)

4√27

c)

8√2

d)

6√3

24.

∛64

a)

8

b)

4∛4

c)

4

d)

16

25.

Simplify
3√6 - 4√6

a)

-√6

b)

√6

c)

-1

d)

Already simplified

26.

Simplify
-11√21 - 11√21

a)

0

b)

-22√21

c)

√21

d)

Already simplified

27.

Simplify
-10√7 + 12√7

a)

-2

b)

-2√7

c)

2√7

d)

Already simplified

28.

Simplify
-10√11 - 11√11

a)

1√11

b)

-21√11

c)

-12√11

d)

Already simplified

29.

Simplify
-3√6 + 3√6

a)

0

b)

√6

c)

-6√6

d)

Already simplified

30.

Simplify
3√8 + 3√2

a)

9√2

b)

6√10

c)

5√2

d)

Already simplified

31.

Simplify
-3√20 - √5

a)

-4√5

b)

-4√15

c)

-7√5

d)

Already simplified

32.

Simplify
3√18 - 2√2

a)

7√2

b)

√16

c)

√2

d)

Already simplified

33.

Simplify
9√2 + 12√3

a)

21√5

b)

21√2

c)

21√3

d)

Already simplified

34.

Simplify
3√5 + √20 - √45

a)

3√-20

b)

2√-20

c)

3√5

d)

2√5

35.

Simplify

$\sqrt[]{72}$

a)

$2\sqrt[]{6}$

b)

$36\sqrt[]{2}$

c)

$6\sqrt[]{2}$

d)

$2\sqrt[]{36}$

e)

12

36.

Simplify:

$\sqrt{63}$

a)

$9\sqrt{7}$

b)

$6\sqrt{2}$

c)

$7\sqrt{6}$

d)

$3\sqrt{7}$

37.

Add

$2\sqrt[]{5}+4\sqrt[]{5}$

a)

$6\sqrt[]{10}$

b)

$8\sqrt[]{10}$

c)

$8\sqrt[]{5}$

d)

$6\sqrt[]{5}$

38.

Add the radicals below

$\sqrt[]{5}+\sqrt[]{20}$

Hint: Simply $\sqrt[]{20}$ first.

a)

5

b)

$5\sqrt[]{5}$

c)

$3\sqrt[]{5}$

d)

10

39.

Subtract the radical expressions below

$-13\sqrt[]{11}-13\sqrt[]{11}$

a)

$-26\sqrt[]{11}$

b)

$-\sqrt[]{11}$

c)

$-13\sqrt[]{11}$

d)

$-26\sqrt[]{22}$

40.

Subtract the radical expressions below

$4\sqrt[]{12}-5\sqrt[]{27}$

Hint: SImplify $\sqrt[]{12}$ and $\sqrt[]{27}$ first. Look back to slide 3, if needed.

a)

$-7\sqrt[]{39}$

b)

$-7\sqrt[3]{3}$

c)

$-\sqrt[]{15}$

d)

$-7\sqrt[]{3}$

41.

Add the radical expressions below and simplify the result.

$9\sqrt[]{2}+12\sqrt[]{3}$

a)

$21\sqrt[]{5}$

b)

$21\sqrt[]{2}$

c)

$21\sqrt[]{3}$

d)

Already simplified. One cannot add these since the two radicands are simplified and are not exactly the same.

42.

Multiply the radical expressions and simplify the result.

$\sqrt[]{5}\cdot\sqrt[]{10}$

a)

$\sqrt[]{50}$

b)

$2\sqrt[]{5}$

c)

$5\sqrt[]{2}$

d)

50

43.

Multiply the radical expressions and simplify the result.

$4\sqrt{6}\cdot\sqrt{3}$

a)

$4\sqrt{9}$

b)

$\sqrt{72}$

c)

$4\sqrt{18}$

d)

$12\sqrt{3}$

44.

Multiply the radical expressions and simplify the result.

$-3\sqrt[]{2}\cdot5\sqrt[]{3}$

a)

$15\sqrt[]{6}$

b)

$-15\sqrt[]{6}$

c)

$-8\sqrt[]{6}$

d)

Already simplified

45.

Multiply and simplify:

$\sqrt[]{6}\cdot\sqrt[]{6}$

a)

$\sqrt[]{36}$

b)

$2\sqrt[]{3}$

c)

$\sqrt[]{6}$

d)

6

46.

Multiply and simplify

$\sqrt[]{3}\cdot\sqrt[]{15}$

a)

$3\sqrt[]{5}$

b)

$5\sqrt[]{3}$

c)

$9\sqrt[]{5}$

d)

$\sqrt[]{45}$

47.

Simplify √30 ⋅ √20

a)

√600

b)

5√2

c)

10√6

d)

2√150

48.

Simplify -2√10 ⋅ 3√20

a)

-60√2

b)

10√2

c)

√30

d)

-6√200

49.

Simplify:
6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

50.

(-2√7)(3√28)

a)

-6√14

b)

6√13

c)

-84

d)

-78

51.

Simplify:
(8√10)(√3)

a)

8√30

b)

16√15

c)

24√10

d)

8√3

52.

Simplify:
(4√5)(7√7)

a)

28√35

b)

4√35

c)

140√7

d)

Cannot be multiplied.

53.

Simplify:
(2√2)(3√10)

a)

6√20

b)

12√5

c)

2√5

d)

8√5

54.

Multiply

$\left(2\sqrt{12}\right)\left(3\sqrt{7}\right)$ *Remember to simplify*

a)

$6\sqrt{84}$

b)

$5\sqrt{19}$

c)

$12\sqrt{21}$

d)

$8\sqrt{10}$

55.

Multiply the radical expressions together.

$5\sqrt[]{2}\cdot7\sqrt[]{3}$

a)

$12\sqrt[]{5}$

b)

$10\sqrt[]{21}$

c)

$35\sqrt[]{6}$

d)

$35\sqrt[]{5}$

56.

Multiply the radical expressions together.

$5\sqrt[]{2}\cdot7\sqrt[]{3}$

a)

$12\sqrt[]{5}$

b)

$10\sqrt[]{21}$

c)

$35\sqrt[]{6}$

d)

$35\sqrt[]{5}$

57.

Is the following number rational or irrational? (77/3)

a)

Rational

b)

Irrational

58.

Is the following number rational or irrational? (π / 2)

a)

Rational

b)

Irrational

59.

Is the following number rational or irrational? (π)

a)

Rational

b)

Irrational

60.

Once simplified, is this number rational or irrational? (√2) * (√2)

a)

Rational

b)

Irrational

61.

The sum of a rational and irrational number is always....

a)

Rational

b)

Irrational

62.

Which is NOT always true....

a)

The sum of a rational and irrational is irrational

b)

The Product of a rational and a rational is rational

c)

The Product of an irrational and irrational is irrational

d)

The sum of two irrational numbers is irrational

63.

A non-perfect square is which type of number?

a)

Rational

b)

Irrational

64.

A perfect square is which type of number?

a)

Rational

b)

Irrational

65.

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 fraction.

c)

A rational number cannot be a repeating decimal.

66.

Is the result rational or irrational? Explain.

a)

Rational; The sum of two rationals is always rational.

b)

Irrational; The sum of a rational and an irrational is always irrational.

c)

Rational; The product of two rationals is always rational.

d)

Irrational; The product of a nonzero rational and an irrational is always irrational.

67.

$\sqrt{7}\cdot\ \sqrt{3}\ =\ ?,\ which\ is\ ?$

a)

Sum of rational and irrational, so it is irrational

b)

Sum of two irrationals, so it is irrational

c)

Product of two irrationals, so it is irrational

d)

Product of two rationals, so it is rational

68.

$7\frac{6}{10}\cdot\ 3\ =\ ?,\ which\ is\ ?$

a)

Sum of rational and irrational, so it is irrational

b)

Sum of two irrationals, so it is irrational

c)

Product of rational and irrational, so it is irrational

d)

Product of two rationals, so it is rational

69.

$3+2\sqrt{5}\ =\ ?,\ so\ the\ result\ is\ ?$

a)

Sum of rational and irrational, so it is irrational

b)

Sum of two irrationals, so it is irrational

c)

Product of two irrationals, so it is irrational

d)

Product of two rationals, so it is rational

70.

a)

y

b)

y²

c)

√y

d)

y√0

71.

a)

x³√x

b)

7x√x²

c)

x⁶√x

d)

√x

72.

a)

xy√y

b)

x²y²√y

c)

xy√xy

d)

2x2y√y

73.

a)

x⁴y⁴√y

b)

72xy

c)

xy√y

d)

x²y³√x²

74.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

75.

-3√20x⁴y²

a)

-6x²y√5

b)

6xy√5

c)

-3xy√2

d)

3x²y√5

76.

a)

A

b)

B

c)

C

d)

D

77.

a)

A

b)

B

c)

C

d)

D

78.

a)

A

b)

B

c)

C

d)

D

79.

a)

A

b)

B

c)

C

d)

D

80.