Free Printable Square and Square roots & Cube and Cube roots

1.

During a mass drill exercise, 6250 students of different

schools are arranged in rows such that the number of

students in each row is equal to the number of rows. In

doing so, the instructor finds out that 9 children are left

out. Find the number of children in each row of the square.

a)

69

b)

89

c)

79

d)

81

2.

Find the least number that must be added to 8974 so as

to get a perfect square.

a)

49

b)

50

c)

52

d)

51

3.

Find the smallest number that can be multiplied to 1620

to get a perfect square.

a)

2

b)

3

c)

4

d)

5

4.

The one's digit of cube of 27 is

a)

9

b)

7

c)

3

d)

8

5.

If one of the member of Pythagorean triplet is 24, then the other two members are

a)

143,145

b)

143,144

c)

144,145

d)

10,25

6.

Which of the following is a perfect cube ?

a)

175616

b)

171656

c)

561716

d)

157616

7.

Find the smallest number by which 9720 must be divided to get a perfect cube ?

a)

5

b)

3

c)

15

d)

45

8.

Find the sum of following odd numbers :

111+113+115+117+119+121+123+125+127+129+131

a)

1728

b)

1331

c)

1000

d)

2197

9.

The difference of two perfect cube is 2716. If the cube root of smaller of the two number is 13, then find the cube root of larger number.

a)

16

b)

19

c)

17

d)

18

10.

A king wanted to reward his advisor, a wise man of the kingdom. So he asked the Wiseman to name his own reward. The Wiseman thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, three coins for the second day, five coins for the third day and so on for thirty one days. Without making calculations, find how many coins will the advisor get in that month?

a)

841

b)

941

c)

961

d)

861

11.

How many numbers lie between the squares of 27 and 28 ?

a)

54

b)

55

c)

56

d)

none of these

12.

If one of the member of Pythagorean triplet is 50, then the other two members are

a)

7,48

b)

624,626

c)

624,625

d)

14,48

13.

Find the smallest square number which is divisible by each of the numbers 6, 9 and 15.

a)

841

b)

900

c)

961

d)

784

14.

Find the least number that must be subtracted from 8974 so as to get a perfect square.

a)

138

b)

136

c)

135

d)

137

15.

Three numbers are in the ratio 2:3:4 and the sum of their cube is 0.334125. The numbers are

a)

28,42,56

b)

30,45,60

c)

26,39,52

d)

none of the above

16.

If one member of Pythagorean triplet is 2m, then the other two members are

a)

m , m²+1

b)

m²+1 , m²-1

c)

m² , m²+1

d)

m² , m²-1

17.

The difference of squares of 62 and 63 is

a)

125

b)

124

c)

126

d)

none of the above

18.

The value of $\sqrt{760+\sqrt{560+\sqrt{239+\sqrt{289}}}}$

a)

26

b)

27

c)

28

d)

29

19.

If a number has ___,____,_____ and ____ in its unit's place it is not a perfect square

a)

2,3,5,8

b)

2,3,6,9

c)

2,3,7,8

d)

2,4,7,9

20.

The square of 19 is

a)

371

b)

471

c)

361

d)

461

21.

Which of the following numbers would have digit 6 at unit place.

a)

19²

b)

24²

c)

25²

d)

57²

22.

The number of zeros in the square of 70 is

a)

2

b)

4

c)

3

d)

5

23.

The number of non-square numbers between 56²and 57² is

a)

102

b)

112

c)

114

d)

104

24.

1+3+5+7+9+11+13+15+17 =

a)

100

b)

79

c)

89

d)

81

25.

Express 15² as the sum of consecutive integers.

a)

125 + 126

b)

113+114

c)

112+113

d)

124+125

26.

2² + 3²+ 6² = 7²

9² + 10²+ 90² = 91²

11² + 12² + _______² = ____²

(a)

27.

95² = (a)

28.

Pythagorean triplet whose one member is 12 is

a)

12,13,15

b)

3,4,12

c)

4,6,12

d)

12,35,37

29.

The least number by which 675 should be divided to make it a perfect square is (a)

30.

The smallest number that should be subtracted from 5839 to make it a perfect square is (a)

31.

The prime factors of 405 are:

a)

9 X 9 X 5

b)

3 X 9 X 5

c)

3 X 3 X 3 X 3 X 5

32.

Which statement is NOT true?

a)

√169 = 13

b)

15² = 225

c)

4² = √16

d)

√324 = 18

33.

The sum of 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 is

a)

64

b)

81

c)

56

d)

49

34.

What is the value of $\sqrt{1.44}$

a)

1.2

b)

0.12

c)

12

35.

Find the value of $\sqrt[]{248\ +\sqrt[]{52\ +\ \sqrt[]{144}}}$

a)

-16

b)

$\pm16$

c)

16

d)

16.2

36.

What is the least number by which 384 should be multiplied to make it a perfect square?

a)

2

b)

6

c)

3

37.

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

38.

The area of a square is 117 square meters. Which best represents the length of a side of the square?

a)

10.8 m

b)

11 m

c)

10 m

d)

11.2 m

39.

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

40.

Which is the greatest 4-digit perfect square?

a)

(a) 9999

b)

(b) 9990

c)

(c) 9800

d)

(d) 9801

41.

1. Which is the greatest three-digit perfect square?

a)

(a) 999

b)

(b) 961

c)

(c) 962

d)

(d) 970

42.

The square of which of the following would be even number?

a)

(a ) 2826

b)

( b ) 7779

c)

( c ) 1057

d)

( d ) 131

43.

The square of which of the following would be odd number?

a)

( a) 431

b)

( b) 272

c)

( c) 1234

d)

( d ) 7928

44.

What will be the number of zeros in the square of 400 ?

a)

( a) 5

b)

( b) 1

c)

( c ) 3

d)

( d ) 4

45.

The perfect square number between 30 and 40 is :

a)

( a) 35

b)

( b ) 39

c)

( c ) 36

d)

( d ) 32

46.

In a school parade, students will have to form a square if there are 735 students in the school . How many students won't be a part of it?

a)

14

b)

24

c)

6

d)

8

47.

Rahul’s age is two more than the square root of the age of Mohan’s father. Mohan’s father is 64 years old.Find Rahuls age.

a)

14

b)

24

c)

10

d)

8

48.

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

a)

64

b)

27

c)

81

d)

16

49.

The numbers 1,8,27,64....are called ___

a)

Perfect square

b)

Perfect cube

c)

Not a perfect cube

d)

Not a perfect square

50.

What is the cube number of 6?

a)

64

b)

125

c)

216

d)

343

51.

What is the cube number of 9?

a)

343

b)

125

c)

729

d)

512

52.

What is the cube number of 12?

a)

1334

b)

1728

c)

1738

d)

1564

53.

What is the cube number of 15?

a)

625

b)

3345

c)

3375

d)

2235

54.

Cube of all odd numbers are ___

a)

Even

b)

Odd

55.

Cube of all even numbers are ___

a)

Even

b)

Odd

56.

Numbers ending with digits 4,5,6 and 9,their cubes also end with ___digit

a)

Same

b)

Different

57.

If a number ending with digits 2 and their cubes end with ___

a)

2

b)

5

c)

8

d)

7

58.

Numbers ending with digits 8 and their cubes end with __

a)

2

b)

8

c)

5

d)

7

59.

The cube of negative number is ___

a)

Positive

b)

Negative

c)

Zero

60.

Find the cubes of the following numbers:40

a)

16000

b)

64000

c)

6400

d)

10600

61.

Find the cube root of 551368?

a)

81

b)

82

c)

89

d)

85

62.

Find the cube root of 343000

a)

50

b)

70

c)

90

d)

80

63.

Find the cube root of 729000

a)

80

b)

90

c)

95

d)

93

64.

The cube of a two digit number has four to six digits?

a)

True

b)

False

65.

Cube of a positive number is negative

a)

True

b)

False

66.

A perfect cube does not end with two zeroes

a)

True

b)

False

67.

The cube of natural number of form (3n+1) is also a natural number of form (3n+1)

a)

True

b)

False

68.

Find the cube root of 1331

a)

11

b)

12

c)

21

d)

31

69.

The one’s digit of the cube of 53 is:

a)

9

b)

3

c)

7

d)

1

70.

Which of the following is not a perfect cube?

a)

216

b)

1000

c)

243

d)

1331

71.

By what number should 81 be divided to get a perfect cube?

a)

3

b)

6

c)

7

d)

9

72.

By what number should we divide 135 to get a perfect cube?

a)

3

b)

5

c)

7

d)

9

73.

Cube root of 15625 is:

a)

5

b)

15

c)

25

d)

35

74.

What should be divided by 53240 to make it a perfect cube?

a)

5

b)

10

c)

15

d)

20

75.

The value of 43√1000 is:

a)

400

b)

40

c)

10

d)

4

76.

A perfect cube of a number having 0 at its unit place, ends with _____ zeros.

a)

1

b)

2

c)

3

d)

4

77.

What is the cube of 2a?

a)

$2a^3$

b)

$4a^3$

c)

$8a^3$

d)

$16a^3$

78.

When the square of a number is subtracted from the cube of the same number, it becomes 100. Find the number.

a)

1

b)

2

c)

4

d)

5

79.

Which is the smallest natural number by which 243 must be multiplied to make the product a perfect cube?

a)

3

b)

9

c)

8

d)

7

80.

Apala makes a cuboid of plasticine of sides 5 cm, 4 cm, 2 cm. How many such cuboids will be needed to form a cube ?

a)

20

b)

25

c)

10

d)

15

Square and Square roots & Cube and Cube roots

Total questions: 80

Worksheet time: 3600secs

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