Free Printable Square, Cubes and their Roots

1.

$\sqrt{16}=?$

a)

8

b)

2

c)

4

d)

32

2.

$3_{\sqrt{8}}$ (cube root of 8)

a)

2

b)

$\pm2$

c)

-2

d)

None of the above

3.

$\left(-6\right)^2$ = ?

a)

12

b)

-12

c)

-36

d)

36

4.

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

a)

$\frac{8}{27}$

b)

$\frac{8}{9}$

c)

$\frac{4}{9}$

d)

$\frac{4}{3}$

5.

Which of the following are examples of perfect squares?

a)

4

b)

6

c)

9

d)

25

6.

27 is a perfect cube

a)

true

b)

false

7.

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

a)

true

b)

false

8.

$\sqrt{36}=$

a)

4

b)

9

c)

6

d)

12

9.

$3\sqrt{64}=$

a)

8

b)

5

c)

4

d)

12

10.

Select all the PERFECT SQUARES

a)

10

b)

144

c)

9

d)

8

11.

Select all the PERFECT CUBES

a)

8

b)

2

c)

125

d)

27

12.

Squaring a number means multiplying a number by itself.

a)

True

b)

False

13.

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

a)

True

b)

False

14.

Evaluate. 8³

a)

512

b)

398

c)

43

d)

764

15.

Solve.
√9 × √100

a)

30

b)

-200

c)

900

d)

90

16.

$7^2$ equals

a)

49

b)

14

17.

$5^2$ equals

a)

25

b)

10

18.

$10^2$ equals

a)

100

b)

20

19.

$\sqrt[]{64}$ equals

a)

8

b)

32

20.

$\sqrt[]{16}$ equals

a)

4

b)

8

21.

$\sqrt[]{36}$ equals

a)

6

b)

18

22.

$3^3$ equals

a)

27

b)

9

23.

$2^3$ equals

a)

8

b)

6

24.

$4^3$ equals

a)

64

b)

12

25.

$9^2$ equals

a)

81

b)

18

26.

$\sqrt[]{144}$ equals

a)

12

b)

72

27.

$5^3$ equals

a)

125

b)

15

28.

$\sqrt[3]{216}$ equals

(a)

29.

$\sqrt[3]{125}$ equals

(a)

30.

$\sqrt[3]{1,000}$ equals

(a)

31.

$9^2=18$ True or false?

a)

True

b)

False

32.

$-\sqrt{144}$

a)

12

b)

-12

c)

-72

d)

none of the above (imaginary number)

33.

$3_{\sqrt{8}}$ (cube root of 8)

a)

2

b)

$\pm2$

c)

-2

d)

None of the above

34.

The area of a square painting is 81 $cm^2$ . What is the length of one side?

a)

9

b)

-9

c)

40.5

d)

-40.5

35.

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

a)

$\frac{8}{27}$

b)

$\frac{8}{9}$

c)

$\frac{4}{9}$

d)

$\frac{4}{3}$

36.

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

37.

Arihaan, Viraav, and Arathana are solving math problems to win a race. They need to determine the approximate value of $\sqrt{47}$ . Viraav insists the value is closer to 7, while Arathana is sure it is closer to 8. Arihaan thinks the value is closer to 6. Who do you agree with?

a)

Arihaan

b)

Viraav

c)

Arathana

d)

None of them

38.

13²

a)

26

b)

196

c)

144

d)

169

39.

Is 225 a perfect square?

a)

Yes

b)

No

40.

$^3\sqrt{1}=$

a)

1

b)

-1

c)

±1

d)

none

41.

The number 1,000 is a...

a)

perfect square

b)

perfect cube

42.

$^3\sqrt{\frac{1000}{343}}=$

a)

100/7

b)

10/7

c)

10/49

d)

100/49

43.

What is a square?

a)

Something you multiply by the 3rd power

b)

A shape

c)

A number you multiply by itself

44.

Solve.
√9 × √100

a)

30

b)

-200

c)

900

d)

90

45.

Select all perfect cubes

a)

2

b)

8

c)

27

d)

64

e)

9

46.

What is the answer for this sum?

1331^{0.3\overline{3}}

a)

11

b)

13

c)

39

d)

443.6

47.

What will be the value of 5, given that 5³ equates to 125?

a)

125⁵

b)

125^-3

c)

125^1/3

d)

log₃(125)

48.

Difference between 2 consecutive cube numbers (n)³and (n-1)³

a)

n(n-1)+1

b)

1 + 3n(n-1)

c)

3n(n-1)(n+1)

d)

3n - 3824

49.

Difference between 2 consecutive square numbers (n)² & (n+1)²

a)

2n + 1

b)

n²+ 1

c)

n²- 1

d)

2n - 1

50.

Which of these is NOT a perfect square?

(a) 3721 (b) 512 (c) 729

a)

(a) only

b)

(b) only

c)

(b) & (c) only

d)

None of these

51.

Estimate the Cube Root of 389017

a)

73

b)

77

c)

79

d)

623

52.

The area of one face of a cube is 64 sq. cm, find the:

(a) Length of Edge
(b) Volume of Cube

a)

(a) 4 cm, (b) 512 cu. cm

b)

(a) 4 cm, (b) 64 cu. cm

c)

(a) 8 cm, (b) 64 cu. cm

d)

(a) 8 cm, (b) 512 cu. cm

53.

Answer: $\sqrt{\left(64\right)^{\frac{1}{3}}}$

a)

2

b)

4

c)

8

d)

16

54.

What is the square root of 7396?

a)

76

b)

84

c)

86

55.

What is the least number to multiply 42 in order to get a perfect square?

a)

3 x 2 = 6

b)

2 x 5 = 10

c)

7 x 2 x 3 = 42

d)

27372 x 0 = 0

56.

Determine which is perfect square?

a)

54

b)

36

c)

21

d)

43

57.

$9^2=18$ True or false?

a)

True

b)

False

58.

$\sqrt{-144}$

a)

12

b)

-12

c)

72

d)

none of the above (imaginary number)

59.

Choose which is perfect square?

(Have 2 answers)

a)

514

b)

225

c)

908

d)

576

60.

$-6^2$ = ?

a)

36

b)

-36

c)

12

d)

-12

61.

$32^2-13^2$

a)

855

b)

456

c)

988

d)

856

62.

$\left(-\frac{5}{6}\right)^3$

a)

$\frac{25}{36}$

b)

$\frac{125}{216}$

c)

$-\frac{36}{25}$

d)

$\frac{36}{25}$

63.

estimate a square root of a number $\sqrt{54}$

a)

$=7$

b)

$\approx7$

c)

$\ne7$

d)

$\cong7$

64.

Which of the following is irrational?

a)

$\sqrt{49}$

b)

$\sqrt{50}$

c)

$\sqrt{81}$

d)

$\sqrt{121}$

65.

$^3\sqrt{64}=$

a)

-8

b)

8

c)

16

d)

4

66.

$^3\sqrt{-64}=$

a)

-8

b)

8

c)

-4

d)

4

67.

$\sqrt{\frac{16}{81}}$ =

a)

4/9

b)

8/27

c)

8/9

d)

4/3

68.

$\sqrt{0.81}=$

a)

0.9

b)

0.27

c)

0.09

d)

0.3

69.

Write an equation for this phrase, "The square root of x is equal to 3."

a)

x² = 3

b)

x² = 9

c)

√x = 3

d)

√x = 9

70.

Solve for p when p² = 100.

a)

1,000

b)

10

c)

0.10

d)

-0.10

71.

Write an equation for this phrase, "2 cubed is equal to the square root of x."

a)

2³ = √x

b)

2² = √x

c)

4 = √16

d)

√x = 2

72.

73²+ 21=

a)

5850

b)

5350

c)

9843

d)

1243

73.

Given the volume, find the length of each side of the cube.

a)

16

b)

16 ft

c)

18

d)

18 ft

74.

In an epidemic, the number of patients suffering the disease increases according to the power of three of the day, where $1^3$ patients on the first day, $2^3$ patients on the second day, $3^3$ patients on the third day and so on.

What is the total of patients suffering the disease after 5 days?

(a)

75.

Approximate the square root to the tenths place: √52

a)

7.2

b)

7.3

c)

7.1

d)

7.5

76.

What is a square?

a)

Something you multiply by the 3rd power

b)

A shape

c)

A number you multiply by itself

77.

Square root of 16 is....

a)

8

b)

4

c)

2

d)

3

78.

True or false? 9² is 18

a)

True

b)

False

79.

Is 225 a perfect square?

a)

Yes

b)

No

80.

The square root of 256 is...

a)

15

b)

18

c)

13

d)

16

81.

-√144

a)

12

b)

13

c)

-12

d)

None of the above

82.

b²=361
b=...

a)

19

b)

20

c)

16

d)

17

83.

4

a)

Is a perfect square.

b)

Is not a perfect square.

84.

∛8

a)

2

b)

-2

c)

±2

d)

None

85.

Find the cube root(s): ∛1

a)

1

b)

-1

c)

±1

d)

none

86.

The area of a square painting is 81 cm². What is the side length of the painting?

a)

40.5 cm

b)

162 cm

c)

6,561 cm

d)

9 cm

87.

Solve.
√9 × √100

a)

30

b)

-200

c)

900

d)

90

88.

The number 1,000 is a...

a)

perfect square

b)

perfect cube

89.

$^3\sqrt{64}=$

a)

-8

b)

8

c)

16

d)

4

90.

Select all perfect cubes

a)

2

b)

8

c)

27

d)

64

e)

9

91.

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

a)

4/9

b)

2/3

c)

6/9

d)

8/27

92.

Write an equation for this phrase, "The square root of x is equal to 3."

a)

x² = 3

b)

x² = 9

c)

√x = 3

d)

√x = 9

93.

Write an equation for this phrase, "2 cubed is equal to the square root of x."

a)

2³ = √x

b)

2² = √x

c)

4 = √16

d)

√x = 2

94.

Select the answer with all perfect squares.

a)

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

b)

9, 50, 75, 81, 100

c)

9, 50, 81, 100

d)

9, 81,100

95.

What is the cube root of 125?

a)

5

b)

-5

c)

25

d)

-25

96.

$\sqrt{16}=?$

a)

8

b)

2

c)

4

d)

32

97.

$9^2=18$ True or false?

a)

True

b)

False

98.

$-\sqrt{144}$

a)

12

b)

-12

c)

-72

d)

none of the above (imaginary number)

99.

$\sqrt{-144}$

a)

12

b)

-12

c)

72

d)

none of the above (imaginary number)

100.

$3_{\sqrt{8}}$ (cube root of 8)

a)

2

b)

$\pm2$

c)

-2

d)

None of the above

101.

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

a)

$\pm1$

b)

1

c)

-1

d)

none of the above (imaginary number)

102.

The area of a square painting is 81 $cm^2$ . What is the length of one side?

a)

9

b)

-9

c)

40.5

d)

-40.5

103.

$-6^2$ = ?

a)

36

b)

-36

c)

12

d)

-12

104.

$\left(-6\right)^2$ = ?

a)

12

b)

-12

c)

-36

d)

36

105.

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

a)

$\frac{8}{27}$

b)

$\frac{8}{9}$

c)

$\frac{4}{9}$

d)

$\frac{4}{3}$

106.

Solve for p when $p^2=100$

a)

$\pm10$

b)

10

c)

$\pm1,000$

d)

1,000

107.

Solve for x when $x^3=\frac{1}{8}$

a)

2

b)

$\frac{1}{64}$

c)

$\frac{1}{3}$

d)

$\frac{1}{2}$

108.

Write an equation for the phrase "Two cubed is equal to the square root of x".

a)

$4=\sqrt{16}$

b)

$2^2=\sqrt{x}$

c)

$2^{3\ }=\sqrt{x}$

d)

$\sqrt{x}=2$

109.

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

110.

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

111.

Which of the following is irrational?

a)

$\sqrt{49}$

b)

$\sqrt{50}$

c)

$\sqrt{81}$

d)

$\sqrt{121}$

112.

73²+21=

a)

5850

b)

5350

c)

9843

d)

1243

113.

$\left(-\frac{5}{6}\right)^3$

a)

$\frac{25}{36}$

b)

$\frac{-\ 125}{216}$

c)

$-\frac{36}{25}$

d)

$\frac{36}{25}$

114.

The number 1,000 is a...

a)

perfect square

b)

perfect cube

115.

$^3\sqrt{\frac{1000}{343}}=$

a)

100/7

b)

10/7

c)

10/49

d)

100/49

116.

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

117.

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

118.

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.

119.

Find the sum of 1+3+5+7+9+11+13+15+17+19

a)

81

b)

121

c)

100

d)

144

120.

Write a Pythagorean triplet whose one number is 12.

a)

(12,36,38)

b)

(12,24,27)

c)

(12,16,19)

d)

(12,35,37)

121.

If

\sqrt{1521}

= 39, find the value of

\sqrt{0.1521\ }\ \ +\ \ \sqrt{15.21}

a)

42.9

b)

4.29

c)

3.51

d)

35.1

122.

$9^2=18$ True or false?

a)

True

b)

False

123.

$-\sqrt{144}$

a)

12

b)

-12

c)

-72

d)

none of the above (imaginary number)

124.

The area of a square painting is 81 $cm^2$ . What is the length of one side?

a)

9

b)

-9

c)

40.5

d)

-40.5

125.

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

126.

Determine which is perfect square?

a)

54

b)

36

c)

21

d)

43

127.

What number, n, cubed is equal to 64?

n³ = 64

a)

4

b)

2

c)

8

d)

262,144

128.

Which number is both a perfect square and a perfect cube?

a)

64

b)

27

c)

81

d)

16

129.

∛216

a)

6

b)

72

c)

108

d)

4

130.

Mrs. Hiltz and Ms. Weber decide to host a lemonade stand. The table they use has side lengths of 5 feet. What is the area of their table?

a)

25 feet

b)

25 square inches

c)

5 ft²

d)

25 square feet

131.

Mr. Jarowski is hanging a square picture frame that has ab area of 169 cm². Find the side length of the frame.

a)

12 cm

b)

13 cm

c)

13 in

d)

16 cm

132.

Mr. Woodside is building a garden outside of Walker-Grant Middle School. He has enough fertilizer to cover 121 square feet. If Mr. Woodside wants to make a square garden, what should the length of each side be?

a)

12ft

b)

121ft

c)

11ft

d)

13ft

133.

The area of a square garage is 121 square feet. Will it fit a car that measures 13 feet long? Explain.

(a)

134.

Determine which is perfect square?

a)

54

b)

36

c)

21

d)

43

135.

determine which is square root of 144

a)

11

b)

10

c)

12

d)

14

136.

$3\sqrt{216}$

a)

8

b)

9

c)

6

d)

3

137.

$\sqrt{16}=?$

a)

8

b)

2

c)

4

d)

32

138.

$9^2=18$ True or false?

a)

True

b)

False

139.

$3_{\sqrt{8}}$ (cube root of 8)

a)

2

b)

$\pm2$

c)

-2

d)

None of the above

140.

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

a)

$\frac{8}{27}$

b)

$\frac{8}{9}$

c)

$\frac{4}{9}$

d)

$\frac{4}{3}$

141.

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

142.

Is 225 a perfect square?

a)

Yes

b)

No

143.

The number 1,000 is a...

a)

perfect square

b)

perfect cube

144.

Select all perfect cubes

a)

2

b)

8

c)

27

d)

64

e)

9

145.

$^3\sqrt{\frac{1000}{343}}=$

a)

100/7

b)

10/7

c)

10/49

d)

100/49

146.

$^3\sqrt{\frac{1}{216}}=$

a)

1/8

b)

1/6

c)

1/16

d)

1/216

147.

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

a)

4/9

b)

2/3

c)

6/9

d)

8/27

148.

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

a)

true

b)

false

149.

100 is a ____________

a)

Perfect Square

b)

Perfect Cube

c)

Both

d)

Neither

150.

$x^3=1,000.\ \ What\ does\ x=?$

a)

1

b)

100

c)

10

d)

0

151.

$x^3=1,000.\ \ What\ does\ x=?$

a)

1

b)

100

c)

10

d)

0

152.

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

a)

True

b)

False

153.

Squaring a number means multiplying a number by itself.

a)

True

b)

False

154.

True or false? 9² = 18

a)

True

b)

False

155.

Is 225 a perfect square?

a)

Yes

b)

No

156.

13²

a)

26

b)

196

c)

144

d)

169

157.

$-\sqrt{36}=$

a)

-6

b)

6

c)

-18

d)

12

158.

$^3\sqrt{8}=$

a)

2

b)

-2

c)

±2

d)

None

159.

$^3\sqrt{-8}$ =

a)

2

b)

-2

c)

±2

d)

None

160.

$^3\sqrt{1}=$

a)

1

b)

-1

c)

±1

d)

none

161.

The number 1,000 is a...

a)

perfect square

b)

perfect cube

162.

$\sqrt{64}=$

a)

32

b)

8

c)

4

d)

16

163.

$^3\sqrt{64}=$

a)

-8

b)

8

c)

16

d)

4

164.

$^3\sqrt{-64}=$

a)

-8

b)

8

c)

-4

d)

4

165.

6³ = ?

a)

196

b)

206

c)

216

d)

226

166.

Select all perfect cubes

a)

2

b)

8

c)

27

d)

64

e)

9

167.

-6² =

a)

36

b)

-36

c)

12

d)

-12

168.

(-6)² =

a)

36

b)

-36

c)

12

d)

-12

169.

$\sqrt{\frac{16}{81}}$ =

a)

4/9

b)

8/27

c)

8/9

d)

4/3

170.

$\left(\frac{5}{6}\right)^2$ =

a)

25/36

b)

10/12

c)

5/6

d)

52/62

171.

$\sqrt{0.81}=$

a)

0.9

b)

0.27

c)

0.09

d)

0.3

172.

$^3\sqrt{\frac{1000}{343}}=$

a)

100/7

b)

10/7

c)

10/49

d)

100/49

173.

$^3\sqrt{\frac{512}{125}}=$

a)

12/25

b)

6/5

c)

8/5

d)

8/10

174.

$^3\sqrt{\frac{1}{216}}=$

a)

1/8

b)

1/6

c)

1/16

d)

1/216

175.

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

a)

4/9

b)

2/3

c)

6/9

d)

8/27

Square, Cubes and their Roots

Total questions: 175

Worksheet time: 4hrs 23mins

Similar Resources on Wayground