Free Printable Radicals

1.

When adding or subtracting square roots, what number HAS TO BE THE SAME?

a)

The coefficient (number in front of square root)

b)

The radicand (number in square root)

c)

The numbers don't matter

d)

Both have to be the same

2.

√8 - 6√2

a)

-4√2

b)

2√2

c)

-6√6

d)

-6√10

3.

When adding or subtracting square roots, what number HAS TO BE THE SAME?

a)

The coefficient (number in front of square root)

b)

The radicand (number in square root)

c)

The numbers don't matter

d)

Both have to be the same

4.

√8 - 6√2

a)

-4√2

b)

2√2

c)

-6√6

d)

-6√10

5.

√18 + √2

a)

√20

b)

4√5

c)

4√2

d)

10√2

6.

√5 + √20

a)

5

b)

25

c)

3√5

d)

2√3

7.

Simplify the following: 4√5 - 6√5 + 4√3 - 2√3

a)

3√5 - 4√5 + 4√3 - 2√3

b)

-2√5 + 2√3

c)

√3

d)

10√5 + 2√3

8.

Simplify completely.

a)

2√3

b)

-8√3

c)

2√6

d)

-8√6

9.

$3\sqrt{5}+7\sqrt{5}$

a)

$\sqrt{5}$

b)

$10\sqrt{10}$

c)

$10\sqrt{5}$

d)

$21\sqrt{5}$

10.

$2\sqrt{12}-\ 5\sqrt{18}$

a)

$4\sqrt{3}-15\sqrt{2}$

b)

$-3\sqrt{-6}$

c)

$12\sqrt{3}$

d)

$-11\sqrt{2}$

11.

$7\sqrt{50}-2\sqrt{8}$

a)

$5\sqrt{42}$

b)

$31\sqrt{2}$

c)

$15\sqrt{2}$

d)

$27\sqrt{2}$

12.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

13.

2√5 + 4√5 =

a)

6√10

b)

8√10

c)

8√5

d)

6√5

14.

Evaluate
-√3 - 2√12

a)

-11√3

b)

-6√3

c)

-7√3

d)

-5√3

15.

Simplify -√5 - √5

a)

-2√5

b)

0

c)

-2√10

d)

-2√25

16.

a)

√18 + 11√2

b)

22√5

c)

11√20

d)

14√2

17.

What is 11 squared?

11²

a)

132

b)

144

c)

121

d)

22

18.

What is 5 squared?

5²

a)

2.5

b)

25

c)

125

d)

10

19.

What is the square root of 100?

√100

a)

10

b)

200

c)

50

d)

1000

20.

What is the square root of 36?

√ 36

a)

4

b)

6

c)

18

d)

1296

21.

What is 16 squared?

a)

8

b)

256

c)

4

d)

32

22.

The √21 is between which two integers?

a)

5 and 6

b)

20 and 22

c)

4 and 5

d)

10 and 11

23.

2² = _____

a)

2

b)

6

c)

4

d)

16

24.

121 = ______

a)

11²

b)

12

c)

11

d)

112

25.

256 = ______

a)

16³

b)

16²

c)

16

d)

15

26.

√196 = ______

a)

14

b)

14²

c)

15

d)

15²

27.

Find the square root of √144.

a)

18

b)

6

c)

12

d)

24

28.

√ is known as the ___________.

a)

square

b)

radical symbol

c)

radicand

d)

index

29.

What is the square root of √36?

a)

6

b)

9

c)

4

d)

12

30.

Put a mark near where you think you are with square roots (1 - 10)

31.

ARE YOU READY FOR CHALLENGE MODE?

a)

Yes

b)

No

c)

Wut

32.

9³

a)

689

b)

709

c)

729

d)

749

33.

7³

a)

313

b)

323

c)

333

d)

343

34.

What is the cube root of 125?

a)

5

b)

-5

c)

25

d)

-25

35.

a)

9

b)

3

c)

1/3

d)

1

36.

I can simplify radical expressions that include perfect square roots.

Simplify the radical below.

$\sqrt{80}$

a)

$4\sqrt{5}$

b)

$\sqrt{16\cdot5}$

c)

$2\sqrt{20}$

37.

I can simplify radical expressions that include perfect square roots.

Simplify the radical below.

$\sqrt{162}$

a)

$2\sqrt{9}$

b)

$\sqrt{81\cdot2}$

c)

$9\sqrt{2}$

38.

I can simplify radical expressions that include perfect square roots.

Simplify the radical below.

$\sqrt{147}$

a)

$7\sqrt{3}$

b)

$\sqrt{7\cdot3}$

c)

$3\sqrt{7}$

39.

What do you need to find to simplify square roots

a)

perfect square factor

b)

square roots

c)

even factors

d)

factors of ten

40.

What is the largest perfect square that goes into $\sqrt{96}$ ?

a)

4

b)

9

c)

6

d)

16

41.

Simplify $\sqrt{45}$

What is the largest perfect square that is a factor of 45? 9

Write your number as the product of the perfect square and the other number.

$\sqrt[]{9\times5}$

Simplify.

a)

$9\sqrt{5}$

b)

$5\sqrt{9}$

c)

$3\sqrt{5}$

d)

$5\sqrt{3}$

42.

Simplify $\sqrt{84}$

What is the largest perfect square that is a factor of 84? 4

Write your number as the product of the perfect square and the other number.

$\sqrt[]{4\ x\ 21}$

Simplify.

a)

$4\sqrt{21}$

b)

$2\sqrt{21}$

c)

$21\sqrt{2}$

d)

$21\sqrt{4}$

43.

Simplify $\sqrt{150}$

What is the largest perfect square that is a factor of 150? 25

Write 150 as a product of the perfect square and its other factor.

$\sqrt[]{25\times6}$

Simplify.

a)

$5\sqrt{6}$

b)

$6\sqrt{5}$

c)

$10\sqrt{15}$

d)

$3\sqrt{75}$

44.

Select all perfect square factors

a)

9

b)

3

c)

6

d)

64

e)

25

45.

Select all perfect square factors

a)

5

b)

100

c)

144

d)

200

e)

121

46.

Simplify $\sqrt{242}$

What is the largest perfect square that is a factor of 242? 121

Write 242 as factor of the perfect square and the other factor.

$\sqrt[]{121\times2}$

Simplify.

a)

$2\sqrt{11}$

b)

$11\sqrt{2}$

c)

$4\sqrt{23}$

d)

$2\sqrt{11}$

47.

Simplify $\sqrt{54}$

What is the largest perfect square that is a factor of 54? 9

Write 54 as a factor of the perfect square and the other factor.

$\sqrt[]{9\times6}$

Simplify

a)

$9\sqrt{6}$

b)

$6\sqrt{3}$

c)

$6\sqrt{9}$

d)

$3\sqrt{6}$

48.

Simplify Completely $\sqrt{162}$

a)

$2\sqrt{9}$

b)

$9\sqrt{2}$

c)

$6\sqrt{54}$

d)

$3\sqrt{54}$

49.

Which are the best factors to use to simplify $\sqrt{200}$ ?

(a)

50.

Which are the best factors to use to simplify $\sqrt{588}$ ?

(a)

51.

Simplify $\sqrt{500}$

Use either method.

a)

$4\sqrt{125}$

b)

$5\sqrt{10}$

c)

$10\sqrt{5}$

d)

$10\sqrt{50}$

52.

Simplify $\sqrt{108}$

Use either method.

a)

$3\sqrt{6}$

b)

$6\sqrt{3}$

c)

$36\sqrt{3}$

d)

$3\sqrt{36}$

53.

Simplify $\sqrt{147}$

a)

impossible

b)

$3\sqrt{7}$

c)

cookies

d)

$7\sqrt{3}$

54.

Simplify $\sqrt[]{18}$

a)

$3\ \sqrt[]{2}$

b)

$2\ \sqrt[]{3}$

c)

$9\ \sqrt[]{2}$

d)

$2\ \sqrt[]{9}$

55.

Simplify $\sqrt[]{24}$

a)

$6\ \sqrt[]{2}$

b)

$2\ \sqrt[]{6}$

c)

$8\ \sqrt[]{3}$

d)

$3\ \sqrt[]{8}$

56.

Simplify $\sqrt[]{42}$

a)

$\ \sqrt[]{42}$

b)

$7\ \sqrt[]{6}$

c)

$2\ \sqrt[]{21}$

d)

$21\ \sqrt[]{2}$

57.

Simplify $\sqrt[]{72}$

a)

$\ 9\ \sqrt[]{8}$

b)

$36\ \sqrt[]{2}$

c)

$2\ \sqrt[]{6}$

d)

$6\ \sqrt[]{2}$

58.

Simplify $\sqrt[]{84}$

a)

$\ 12\ \sqrt[]{7}$

b)

$21\ \sqrt[]{2}$

c)

$2\ \sqrt[]{21}$

d)

$7\ \sqrt[]{12}$

59.

Simplify $\sqrt[]{120}$

a)

$\ 2\ \sqrt[]{30}$

b)

$12\ \sqrt[]{10}$

c)

$30\ \sqrt[]{2}$

d)

$4\ \sqrt[]{30}$

60.

Simplify $\sqrt[]{240}$

a)

$\ 24\ \sqrt[]{10}$

b)

$4\ \sqrt[]{15}$

c)

$15\ \sqrt[]{4}$

d)

$6\ \sqrt[]{40}$

61.

Simplify $\sqrt[]{320}$

a)

$\ 2\ \sqrt[]{160}$

b)

$40\ \sqrt[]{8}$

c)

$8\ \sqrt[]{5}$

d)

$10\ \sqrt[]{32}$

62.

Simplify $\sqrt[]{28}$

a)

$\ 2\ \sqrt[]{7}$

b)

$4\ \sqrt[]{7}$

c)

$2\ \sqrt[]{14}$

d)

$\ \sqrt[]{28}$

63.

Simplify $\sqrt[]{68}$

a)

$\ 2\ \sqrt[]{17}$

b)

$4\ \sqrt[]{17}$

c)

$14\ \sqrt[]{7}$

d)

$\ \sqrt[]{68}$

64.

\sqrt{42}\cdot\sqrt{154}

a)

$14i\sqrt{33}$

b)

$14\sqrt{33}$

c)

$49\sqrt{33}$

d)

$33\sqrt{14}$

65.

Simplify.
$\sqrt{2}\times5\sqrt{8}$

a)

$20$

b)

$10$

c)

$5\sqrt{4}$

d)

$5\sqrt{2}$

66.

Simplify.
$\sqrt{6}\times\sqrt{2}$

a)

$4\sqrt{3}$

b)

$\sqrt{12}$

c)

$2\sqrt{3}$

d)

$12$

67.

Simplify √3 × √15

a)

3√5

b)

5√3

c)

2√7

d)

√17

68.

Simplify √10 ⋅ √45

a)

3√50

b)

8√2

c)

√450

d)

15√2

69.

Simplify 6√2 ⋅5√14

a)

32√7

b)

60√7

c)

2√7

d)

30√7

70.

\sqrt{42}\cdot\sqrt{154}

a)

$14i\sqrt{33}$

b)

$14\sqrt{33}$

c)

$49\sqrt{33}$

d)

$33\sqrt{14}$

71.

Simplify:

\sqrt{72a^5b^8}

a)

$6ab\sqrt{2ab}$

b)

$6a^2b^4\sqrt{2a}$

c)

$3a^2b^4\sqrt{8a}$

d)

$6a^4b^8\sqrt{2a}$

72.

Simplify:

-2\sqrt{63}\cdot\ 3\sqrt{28}

a)

$-6\sqrt{7}\cdot6\sqrt{7}$

b)

$-6\sqrt{1764}$

c)

$42$

d)

-252

73.

Simplify:

3\sqrt{5c^4d}\cdot\ 2\sqrt{10c^3d^3}

a)

$5c^3d^2\sqrt{2c}$

b)

$6\sqrt{50c^7d^4}$

c)

$30c^3d^2\sqrt{2c}$

d)

$30c^6d^4\sqrt{2c}$

74.

$\left(8-\sqrt{5}\right)\left(8+\sqrt{5}\right)$

a)

$3$

b)

$59$

c)

$69$

d)

$64-\sqrt{5}$

75.

$\left(3+\sqrt{5}\right)^2$

a)

$14$

b)

$9+\sqrt{5}$

c)

$9\sqrt{5}$

d)

$14+6\sqrt{5}$

76.

$\left(5-\sqrt{u}\right)\left(3+\sqrt{u}\right)$

a)

$8+15\sqrt{u}-u^2$

b)

$15+2\sqrt{u}-u$

c)

$15+2\sqrt{u}-u^2$

d)

$16-u$

77.

$\left(4\sqrt{6}+7\sqrt{13}\right)\left(8\sqrt{6}-3\sqrt{13}\right)$

a)

$192+44\sqrt{78}$

b)

$192+68\sqrt{78}-273$

c)

$44\sqrt{78}-81$

d)

$32\sqrt{6}+44\sqrt{78}-12\sqrt{13}$

78.

List the first prime

(a)

79.

List the second prime number

(a)

80.

5 is the 3rd Prime number

a)

True

b)

False

c)

What is a prime?

d)

Who cares?!?!?

81.

The numbers 5 and 6 are:

a)

Both prime numbers

b)

Both multiples of 30

c)

Both factors of 30

d)

A factor pair of 60

82.

What is the square root of 36?

√ 36

a)

4

b)

6

c)

18

d)

1296

83.

The √21 is between which two integers?

a)

5 and 6

b)

20 and 22

c)

4 and 5

d)

10 and 11

84.

The √40 is between which two integers?

a)

39 and 41

b)

6 and 7

c)

5 and 6

d)

19 and 21

85.

Estimate the square root.

a)

3

b)

4

c)

5

d)

6

86.

Which would be the next number in the pattern?
36, 49, 64, 81 __

a)

82

b)

18

c)

64

d)

100

87.

In 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

88.

The area of a square is 36 cm². What is the length of one side?

a)

6 cm

b)

24 cm

c)

9 cm

d)

9 cm

89.

Square roots are the opposite of ____________.

a)

Cube Roots

b)

Squaring

c)

Multiplication

d)

Absolute Value

90.

A perfect square is a number whose square root is ___________.

a)

Even

b)

irrational

c)

Rational

d)

Odd

91.

If you have 196 chairs and you need to arrange them in an equal amount of row and columns, how many chairs will be in each row?

a)

12

b)

13

c)

14

d)

15

92.

Estimate the square root.

a)

4

b)

5

c)

6

d)

7

93.

Which is the best estimate of the square root of 63?

a)

7.1

b)

7.3

c)

7.5

d)

7.9

94.

Which number is irrational?

a)

9.6

b)

√45

c)

3/8

d)

3.4 x 10 ⁵

95.

Which number is rational below?

a)

√20

b)

√64

c)

6π

d)

√7

96.

Irrational numbers...

a)

reduce to π

b)

never end and never repeat

c)

can sometimes be perfect squares

d)

must be negative

97.

What is the approximate value of √12

a)

2

b)

3.5

c)

4.5

d)

6

98.

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.

99.

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

100.

169

a)

Is a perfect square.

b)

Is not a perfect square.

Radicals

Total questions: 100

Worksheet time: 4hrs 36mins

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