Free Printable Test 4: Radicals & Rational/Irrational Numbers REVIEW

1.

$\sqrt{50}$

a)

$5\sqrt{2}$

b)

$\sqrt{5}$

c)

$2\sqrt{5}$

d)

$25\sqrt{2}$

2.

$\sqrt{243}$

a)

$3\sqrt{3}$

b)

$9\sqrt{3}$

c)

$81\sqrt{3}$

d)

$3\sqrt{81}$

3.

$\sqrt{96}$

a)

$16\sqrt{6}$

b)

$2\sqrt{6}$

c)

$4\sqrt{6}$

d)

$\sqrt{2}$

4.

$\sqrt{216}$

a)

$6\sqrt{4}$

b)

$4\sqrt{6}$

c)

$36\sqrt{6}$

d)

$6\sqrt{6}$

5.

$\sqrt{300}$

a)

$3\sqrt{10}$

b)

$2\sqrt{150}$

c)

$100\sqrt{3}$

d)

$10\sqrt{3}$

6.

$\sqrt{40}$

a)

$4\sqrt{10}$

b)

$10\sqrt{4}$

c)

$2\sqrt{10}$

d)

$10\sqrt{2}$

7.

$\sqrt{256}$

a)

$12\sqrt{2}$

b)

$9\sqrt{14}$

c)

16

d)

$18\sqrt{6}$

8.

$\sqrt{63}$

a)

$9\sqrt{7}$

b)

$6\sqrt{2}$

c)

$7\sqrt{6}$

d)

$3\sqrt{7}$

9.

$\sqrt{147}$

a)

$3\sqrt{49}$

b)

$6\sqrt{3}$

c)

$7\sqrt{3}$

d)

$9\sqrt{7}$

10.

$\sqrt{112}$

a)

$4\sqrt{7}$

b)

$16\sqrt{3}$

c)

$16\sqrt{7}$

d)

$4\sqrt{3}$

11.

Simplify the radical...
√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

12.

-3√20x⁴y²

a)

-6x²y√5

b)

6xy√5

c)

-3xy√2

d)

3x²y√5

13.

$\sqrt{192k^7q^8}$

a)

$8q^4\sqrt{3k^7}$

b)

$8k^3q^4\sqrt{3}$

c)

$8k^3q^4\sqrt{3k}$

d)

$8k^7q^8\sqrt{3k}$

14.

In simplest radical form,
√80 is equivalent to

a)

16√5

b)

2√20

c)

4√5

d)

8√5

15.

$\sqrt{4x^7y^5z^9}$ Simplify

a)

$2x^3y^2z^3\sqrt{xy}$

b)

$2z^3\sqrt{x^7y^5}$

c)

$2xyz\sqrt{x^6y^5z^8}$

d)

$2x^3y^2z^4\sqrt{xyz}$

16.

What kind of terms can be added or subtracted? (Check all that apply)

a)

Like terms

b)

Common terms

c)

Terms with the same radicand

17.

Add

\sqrt{2}+3\sqrt{2}

a)

$2\sqrt{2}$

b)

$3\sqrt{4}$

c)

$4\sqrt{2}$

d)

$4\sqrt{4}$

18.

Add

\sqrt{27}+2\sqrt{12}

a)

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

b)

$7\sqrt{3}$

c)

$12\sqrt{3}$

d)

$7\sqrt{6}$

19.

What do you do after you multiply the outside terms and the inside terms?

a)

Simplify

b)

Multiply

c)

Nothing

20.

Multiply

2\sqrt{12}\times3\sqrt{7}

*Remember to simplify*

a)

$6\sqrt{84}$

b)

$5\sqrt{19}$

c)

$12\sqrt{21}$

d)

$8\sqrt{10}$

21.

Which of these involves simplifying? (Check all that apply)

a)

Simplifying

b)

Adding and Subtracting

c)

Multiplying

22.

When do you simplify FIRST?

a)

Multiplying

b)

Adding and Subtracting

23.

$\sqrt{15}=\sqrt{5}\cdot\sqrt{3}$ True or False?

a)

True

b)

False

24.

$\sqrt{50}=25\sqrt{2}$ True or False?

a)

True

b)

False

25.

√75x²

a)

5x²√3

b)

5x

c)

5x√3x

d)

5x√3

26.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

27.

a)

7√3

b)

Can't Simplify

c)

6√15

d)

6√3

28.

Add: 4√7 - 10 √7 + 7√7

a)

-6√7

b)

14√7

c)

-3√14

d)

√7

29.

Simplify: 2√40 - 3√10

a)

5√10

b)

√10

c)

-√30

30.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

31.

(-2√7)(3√28)

a)

-6√14

b)

6√13

c)

-84

d)

-78

32.

Simplify:
√10 ⋅ √45

a)

3√50

b)

8√2

c)

√450

d)

15√2

33.

Simplify.

a)

b)

c)

d)

34.

Read the question carefully and choose the correct answer.

a)

A

b)

B

c)

C

d)

D

35.

What is the square root symbol called?

a)

Radicand

b)

Radical

c)

The house

d)

It doesn't have a name

36.

Identify the parts of the radical

a)radical symbol

b)index

c)radicand

1

2

3

1)

2)

3)

37.

Simplify: $\left(\sqrt{10x}\right)\left(\sqrt{45x}\right)$

a)

$3\sqrt{50x}$

b)

$2x\sqrt{15}$

c)

$x\sqrt{450}$

d)

$15x\sqrt{2}$

38.

Simplify:
$\sqrt{45x^4y^7}$

a)

$3x^2y^3\sqrt{5}$

b)

$9x^2y^3\sqrt{5}$

c)

$3x^2y^3\sqrt{5y}$

d)

3x⁴y⁷

39.

We can only add or subtract radicals if they have the same (a)

Choose from the below words

radical

radicand

index

coefficient

40.

We can only multiply or divide radicals if they have the same .

(a)

Choose from the below words

index

radical

radicand

coefficient

41.

Simplify the expression

a)

100√2

b)

5√160

c)

20√10

d)

It's already simplified

42.

Simplify the expression

a)

3√5y

b)

√135y

c)

9√4y

d)

They aren't like terms

43.

Write an expression for the perimeter in simplest radical form

a)

2√21 in.

b)

12√2 in.

c)

2√8 + 8√2 in.

d)

They aren't like terms

44.

Simplify the expression

a)

120n√3n

b)

24√5n

c)

600n√n

d)

120√3n³

45.

Which is a fully simplified expression for the area of the rectangle?

a)

6 m²

b)

6√2 m²

c)

18√3 m²

46.

What is a perfect square?

a)

A number divided by 4

b)

A number multiplied by itself

c)

A number multiplied by 2

47.

What is 9²?

a)

18

b)

7

c)

11

d)

81

48.

What is the square root of 64?

a)

32

b)

128

c)

8

d)

16

49.

The number under the radical sign or square root sign is called the ______.

a)

radical sign

b)

radicand

c)

factor

d)

exponent

50.

Write the perimeter of the rectangle in simplest radical form.

a)

$5\sqrt{6}+4\sqrt{3}$

b)

$10\sqrt{12}+8\sqrt{6}$

c)

$10\sqrt{6}+8\sqrt{3}$

d)

$20\sqrt{18}$

51.

A rectangle has a length of $2\sqrt{5}$ and the width is $\sqrt{2}+4\sqrt{3}$ . Write the area of the figure in simplified radical form.

a)

$2\sqrt{10}+8\sqrt{8}$

b)

$2\sqrt{10}+8\sqrt{15}$

c)

$2\sqrt{5}+\sqrt{2}+4\sqrt{3}$

d)

$2\sqrt{7}+8\sqrt{8}$

52.

Simplify

a)

x²y√xy

b)

xy

c)

x²y²

d)

Can't Simplify

53.

2√5 - √5 + 4√5 + √3

a)

6√5 + √3

b)

5√5 + √3

c)

6√5

d)

6√3

54.

Simplify:

a)

4√30

b)

√4√30

c)

√2√30

d)

2√30

55.

Simplify
3√2 - 3√18

a)

-4√8

b)

4√9-6√3

c)

5√12

d)

-6√2

56.

Simplify:
6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

57.

a)

-5√1

b)

8√2 + 13√3

c)

21√5

d)

20√5

58.

a)

0

b)

√5

c)

1

d)

-2√15

59.

The square roots of all perfect squares are___________?

a)

integers or whole numbers

b)

irrational

c)

fractions

d)

divisible by 2

60.

a)

0

b)

3∛1

c)

3∛7

d)

3

61.

The square root of 36x² is __________

a)

6

b)

6x

c)

4x

d)

6x²

62.

Simplify: (7√3)²

a)

147

b)

21

c)

63

d)

49√9

63.

Simplify

a)

40

b)

√14

c)

-10√10

d)

2√10

64.

Simplify √r⁷

a)

r√r⁵

b)

r²√r³

c)

r³√r

d)

√r⁷

65.

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.

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.

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.

68.

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.

69.

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.

70.

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.

71.

Is the result rational or irrational? Explain.

a)

Irrational; The sum of two irrationals is always irrational.

b)

Sometimes rational, sometimes irrational; The sum of two irrationals is sometimes rational, sometimes irrational.

c)

Rational; The product of two rationals is always rational.

d)

Sometimes rational, sometimes irrational; The product of two irrationals is sometimes rational, sometimes irrational

72.

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.

73.

$SUM\ of\ \pi\ and\ 6$

a)

Rational

b)

Irrational

74.

A REPEATING decimal is what type of number?

a)

Rational

b)

Irrational

75.

The square root of 57 is ...

a)

rational

b)

irrational

76.

Which of the following number is rational?

a)

$\sqrt{127}$

b)

$\pi$

c)

$2.5$

d)

$8.98763...$

77.

Which of the following numbers is irrational?

a)

$\sqrt{50}$

b)

$\sqrt{36}$

c)

$\sqrt{169}$

d)

$\sqrt{225}$

78.

Select ALL numbers that are irrational.

a)

10

b)

-21

c)

$\pi$

d)

$\frac{10}{2}$

e)

$\sqrt{10}$

79.

Select ALL numbers that are rational.

a)

55

b)

$\sqrt{289}$

c)

$\sqrt{6}$

d)

$\pi$

e)

$6\frac{7}{9}$

80.

Which of the following is an irrational number?

a)

$\sqrt{0}$

b)

$\sqrt{3}$

c)

$1\overline{.36}$

d)

$-0.19$

81.

A rational number

a)

is a number that can be written as a fraction.

b)

is always positive.

c)

can be a repeating decimal.

d)

is a fraction but not a decimal.

82.

Irrational numbers

a)

never end and never repeat.

b)

can be positive or negative.

c)

reduce to $\pi$

d)

are square roots of perfect squares.

83.

A terminating decimal is

a)

rational.

b)

irrational.

84.

The square root of a perfect square is

a)

irrational.

b)

rational.

85.

Identify the rational numbers.

a)

$\sqrt{64}$

b)

$3\pi$

c)

$\frac{4}{5}$

d)

$0.15151515...$

e)

0

86.

Identify the rational numbers.

a)

$\sqrt{120}$

b)

$\sqrt{36}$

c)

$\sqrt{220}$

d)

$\sqrt{1000}$

87.

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

a)

$5\sqrt{10},\ irrational$

b)

$5\sqrt{5},\ irrational$

c)

$6\sqrt{5},\ irrational$

d)

$6\sqrt{10},\ irrational$

88.

$4\pi\ -\ 4\pi\ =\ ?,\ which\ is\ ?$

a)

rational

b)

irrational

89.

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

a)

rational

b)

irrational

90.

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

a)

rational

b)

irrational

91.

includes integers, fractions, terminating and repeating decimals.

a)

Rational Numbers

b)

Irrational Numbers

92.

What type of number is a non-repeating, non-terminating decimal?

a)

irrational

b)

prime

c)

rational

d)

imaginary

93.

$Why\ is\ \sqrt{2}\ irrational?$

a)

The decimal ends.

b)

The decimal repeats.

c)

The decimal goes on forever.

d)

The decimal does not end and does not repeat.

94.

Which statement is NOT true?

a)

Every rational number is a real number.

b)

Every counting number is a whole number.

c)

Every integer is a rational number.

d)

Every decimal number is an irrational number.

95.

Which is an example of the sum of a rational

number and an irrational number that results in

an irrational number?

a)

$\pi+\sqrt[]{10}$

b)

$0.\overline{79}+\pi$

c)

$\sqrt[]{8}+\sqrt[]{24}$

d)

$\frac{\pi}{\pi}+4$

96.

$3\sqrt{2}\cdot2\sqrt{3}\cdot4\sqrt{6}=$

Solve:

a)

$144;\ rational$

b)

$9\sqrt{11};\ irrational$

c)

$864;\ rational$

d)

$18;\ rational$

97.

$2\sqrt{5}\cdot\sqrt{5}=$

Solve:

a)

50; rational

b)

$3\sqrt{5};\ irrational$

c)

$2\sqrt{10};\ irrational$

d)

$10;\ rational$

98.

Solve: $\sqrt{2}\cdot\sqrt{5}=$

a)

$\sqrt{10};\ irrational$

b)

$\sqrt{7};\ irrational$

c)

$\sqrt{3};\ irrational$

d)

$5;\ rational$

99.

$2\sqrt{9}+3\sqrt{4}-\sqrt{5}$

Solve:

a)

$12-\sqrt{5};\ irrational$

b)

$4\sqrt{8};\ irrational$

c)

$2\sqrt{9}+3\sqrt{4}-\sqrt{5};\ irrational$

d)

$30-\sqrt{5};\ rational$

100.

$5\sqrt{11}-3\sqrt{11}$

Solve:

a)

$2\sqrt{11};\ irrational$

b)

$2\sqrt{22};\ rational$

c)

$2;\ rational$

d)

$22;\ rational$

101.

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

Solve:

a)

$4;\ rational$

b)

$\sqrt{8};\ irrational$

c)

$\sqrt{16};\ rational$

d)

$2\sqrt{4};\ irrational$

102.

Classify $\sqrt{121}$

a)

Rational

b)

Irrational

103.

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

a)

Rational

b)

Irrational

104.

Classify $-3.254$

a)

Rational

b)

Irrational

105.

Classify $\sqrt{5}$

a)

Rational

b)

Irrational

106.

Classify $\frac{3}{5}$

a)

Rational

b)

Irrational

107.

A little challenging..but fairly easy to guess:

\pm

a)

addition then subtraction

b)

subtract then add

c)

plus or minus

108.

Which of the following statements is true?

a)

Infinity is a really small number.

b)

There is only one way to show multiplication.

c)

The expression 2²means two is raised to the power of 2.

d)

Pi is a rational number.

Test 4: Radicals & Rational/Irrational Numbers REVIEW

Total questions: 108

Worksheet time: 27hrs 0mins

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