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Q1. If a number m is equal to n³, then the cube root of m is:

• n
• 2n
• -n
• 3n

Solution

If a number m is equal to n³, then the cube root of m is n.

Q2. If the prime factorization of a number is 3x3x3x5x5x5, then its cube root is:

• 9
• 25
• 6
• 15

Solution

Cube root of a number = 3 x 5 = 15.

Q3. The number of cube numbers between the numbers 10 and 200 is ______ .

• 1
• 2
• 3
• 4

Solution

Cube numbers between 10 and 200 are: 27, 64, 125 Thus, the number of cube numbers between the numbers 10 and 200 is 3.

Q4. Which of the following numbers is not a cube number?

• 2197
• 1729
• 512
• 216

Solution

2197 = (13)³512 = (8)³216 = (6)³1729 = 7 × 247The number 1729 is not a cube number as it cannot be expressed as the cube of any number.

Q5. A number multiplied by itself three times is called:

• square number
• cube number
• cube root
• perfect number

Solution

A number multiplied by itself three times is called cube number.

Q6. 13 + 15 + 17 + 19 is a cube of which number?

• 3
• 4
• 5
• 6

Solution

13 + 15 + 17 + 19 = 64, which is cube of 4.

Q7. The cube root of the number 46656 is ______ .

• 32
• 36
• 31
• 38

Solution

Cube root of the number 46656 = 2233 = 36

Q8. 729 is the cube of:

• 9
• 7
• 6
• 19

Solution

Resolving 729 into prime factors, we get 3 x 3 x 3 x 3 x 3 x 3 = 729 (3 × 3)³ = 729 So, 729 is the cube of 9.

Q9. The number of cubes with 2 digits is ______ .

• 1
• 2
• 3
• 4

Solution

Only 27 and 64 are the cube numbers having two digits. The number of cubes with 2 digits is 2.

Q10. Cube of the number 11 is:

• 121
• 1331
• 33
• 333

Solution

11³ = 11 × 11 × 11 = 1331.

Q11. If the square of a number ends in 5, then its cube ends in

• 1
• 5
• 25
• zero

Solution

If the square of a number ends in 5, then the number also ends in 5.It is known that if the digit at one's place of a number is 5, then its cube will also end in 5.Thus, the cube of the number will end in 5.

Q12. The smallest number by which the number 648 must be divided so that the quotient is a perfect cube is 

• 2
• 3
• 4
• 6

Solution

Q13. The smallest number which can be subtracted from 3400 to make it a perfect cube is

• 5
• 10
• 20
• 25

Solution

We know that: 3375 < 3400 < 4096 Where, 3375 = 15³ and 4096 = 16³ Now, we need to subtract a number from 3400 to make it a perfect cube and that number should be the least. So, the cube number which is smaller and closest to 3400 is 3375. Required number to be subtracted = 3400 - 3375 = 25

Q14. Which is the smallest number that must be multiplied with 171500 to make it a perfect cube?

• 2
• 4
• 8
• 16

Solution

Q15. If 1000 = 2 × 2 × 2 × 5 × 5 × 5 then cube root of 1000 is:

• 15
• 8
• 10
• 25

Solution

Cube root of 1000 is 2 × 5 = 10.

Q16. The unit's digit of the cube of the number 135825 is

• 1
• 2
• 5
• 25

Solution

Since we know that the cube of a number ending with 5 also ends with 5. Thus, the unit's digit of the cube of the number 135825 is 5.

Q17. 1³ + 2³ + 3³ + ... + n³ =

• 1 + 2 + 3 + … + n
• 1² + 2² + 3² + ... + n²
• (1 + 2 + 3 + … + n)²
• (1 + 2 + 3 + … + n)³

Solution

1³ + 2³ + 3³ + ... + n³ = (1 + 2 + 3 + … + n)²

Q18. If 2750 - k is a perfect cube, then the smallest value of k is

• 2
• 4
• 6
• 9

Solution

Consider the number 2750. We need to find the smallest number k which must be subtracted from 2750 to make it a perfect cube. Now, a cube number which is nearest to 2750 is 2744 (=14³). Thus, if we subtract 6 from 2750, it becomes a perfect cube. That is, 2750 - 6 = 2744, a perfect cube k = 6

Q19. Cube root of (-2)3x (-3)3is:

• -6
• 6
• 5
• -5

Solution

Cube root of (-2)3x (-3)3= -2 x -3 = 6.

Q20. If the cube root of 4913 is 17 then the cube root of 4.913 is:

• 1.07
• 0.017
• 0.17
• 1.7

Solution

Cube root of 4.913 is 1.7.

Q21. If 26136 x k is a perfect cube, then the smallest value of k is

• 2
• 4
• 9
• 11

Solution

26136 = 2 x 2 x 2 x 3 x 3 x 3 x 11 x 11 Making triplets, we find that the prime factor 11 do not appear in a group of three.To make 26136 a perfect cube, we need to multiply it with 11.Thus, 26136 x 11 is a perfect cube. Hence, the smallest value of k is 11.

Q22. The cube root of the product of  (-8) x (-343) x (125) is:

• -70
• 70
• -35
• 35

Solution

Cube root of (-8) x (-343) x (125) = (-2) x (-7) x 5 = 70

Q23. Cube root of 216 is:

• 4
• 6
• 8
• 5

Solution

Since, 6 6 6 = 216 So the cube root of 216 is 6.

Q24. Which of the following statements is incorrect?

• Cube of an even number is even.
• Cube of an odd number is odd.
• If a² ends in an even number of zeroes, then a³ ends in an odd number of zeroes.
• If n leaves remainder 1 when divided by 3, then n³ also leaves remainder 1 when divided by 3.

Solution

Third statement is incorrect. The correct statement is as follows: If a² ends in an even number of zeroes, then a³ may or may not end in an odd number of zeroes.   Example, 1)  Let a = 10, then, a² = 100 ends with even number of zeroes a³ = 1000 ends with odd number of zeroes     2) Let a = 100, then, a² = 10000 ends with even number of zeroes a³ = 1000000 ends with even number of zeroes Thus, both a² and a³ ends with even number of zeroes.

Q25. What is the units digit of the cube root of the number 17576?

• 2
• 3
• 4
• 6

Solution

The units digit of the cube root of the number 17576 is 6.

Q26. The value of x for which 64 = x³ is ______ .

• 2
• 64
• 16
• 4

Solution

Resolving 64 into prime factors, we get 64 = 2 x 2 x 2 x 2 x 2 x 2 = (2 x 2)³ = 4³

Q27. If the volume of a cubical tank is 125 m³, then its side is:

• 4 m
• 5 m
• 25 m
• 7 m

Solution

Since, 5 5 5 = 125 So the side of cubical tank is 5 m.

Q28. The square of a number is 64. What is its cube root?

• 8
• 4
• 2
• 1

Solution

Q29. The least number that must be multiplied by 72 to make it a cube number is:

• 4
• 6
• 3
• 2

Solution

Writing 72 as a product of prime factors, we have: 72 =2x2x2x3x3 The prime factor 3 does not appear in a group of three. So, the least number with which 72 must be multiplied to make it a perfect cube is 3.

Q30. Which natural number is equal to its cube?

• 1
• 2
• 3
• 4

Solution

1³ = 1Thus, the natural number 1 is equal to its cube.

Q31. The cube root of the product of 8 x 27 x 125 is:

• 17
• 15
• 30
• 20

Solution

Cube root of 8 x 27 x 125 = 2 x 3 x 5 = 30.

Q32. The length, breadth and height of a cuboid are 18 cm, 6 cm and 12 cm respectively. How many such cuboids will be required to make a cube?

• 6
• 12
• 18
• 36

Solution

Volume of the cuboid = 18 cm x 6 cm x 12 cmWe know that volume of a cube is (edge)³. So, to make a cube, (18 x 6 x 12) should be made as a perfect cube.18 x 6 x 12 = 2 x 3 x 3 x 2 x 3 x 2 x 2 x 3= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3Making triplets, we find that prime factors 2 and 3 are left out. So, to make it a perfect cube, we need to multiply it by 2 x 2 x 3 x 3 = 36Thus, 36 x 18 x 6 x 12 =  (36)³ = Volume of cubeThus, the number of cuboids required to make a cube is 36.

Q33. Which of the following numbers is the cube of an even number?

• 32768
• 2058
• 2197
• 42875

Solution

It is known that cubes of even numbers are even.  So, amongst the given numbers, 32768 and 2058 can be the cubes of an even number.  Now, 32768 = (2 × 2 × 2 × 2 × 2)³ 2058= 2 × 3 × (7)³ It can be seen that 2058 is not a perfect cube.  Thus, 32768 is the cube of an even number.  

Q34. What is the smallest number that must be added to the square of 5 to make it a perfect cube?

• 1
• 2
• 5
• 7

Solution

Square of 5 = 25 We know that 8 < 25 < 27Where, 8 = 2³ and 27 = 3³Now, 25 + 2 = 27, a perfect cube. Clearly, the required smallest number that must be added to the square of 5 to make it a perfect cube is 2.

Q35. The cube of number (-2) is:

• 8
• 4
• -4
• -8

Solution

(-2)³= -2x-2x-2 = -8

Q36. If the digit at one's place of a number is 2, then the digit at one's place of its cube is ______ .

• 8
• 14
• 15
• 16

Solution

If the digit at one's place of a number is 2, then the digit at one's place of its cube is 8.

Q37. What is the smallest number by which 1125 may be divided so that the quotient is a perfect cube?

• 3
• 9
• 15
• 25

Solution

Writing 1125 as a product of prime factors, we have: 1125 = 3x3x5x5x5 The prime factor 3 does not appear in a group of three. So, if we divide 1125 by 9, the quotient will become a perfect cube.

Q38. The cube of the number (3) is:

• 9
• 27
• -9
• -27

Solution

Q39. The number -1728 is the cube of the number ______ .

• -12
• 12
• 15
• -15

Solution

Since, -12 x -12 x -12 = -1728 Therefore, -1748 is the cube of the number -12.

Q40. The cube root of the number 15625 is a perfect square of __________.

• 5
• 25
• 15
• 125

Solution

Cube root of 15625 is 25, which is a perfect square of 5.