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NCERT Class 8 Mathematics MCQ
Cubes And Cube Roots
with Answers
Question : The one’s digit of the cube of 53 is:
(a) 9
(b) 3
(c) 7
(d) 1
Answer : (c)Show Answer :
Explanation: 533 = 53 x 53 x 53
33 = 3x3x3 = 27
Hence, at unit place we will get 7.
Recheck: 533 = 53 x 53 x 53 = 148877
Question : The prime factorisation of 64 is:
(a) 2 x 2 x 2
(b) 4 x 4 x 4
(c) 8 x 8 x 8
(d) None of the above
Answer : (b)Show Answer :
Explanation: 64 = 43 = 4 x 4 x 4
Question : Which of the following is not a perfect cube?
(a) 216
(b) 1000
(c) 243
(d) 1331
Answer : (c)Show Answer :
Explanation: 243 = 3 × 3 × 3 × 3 × 3 = 33 × 32
Question : By what number should 81 be divided to get a perfect cube?
(a) 3
(b) 6
(c) 7
(d) 9
Answer : (a)Show Answer :
Explanation: The prime factorisation of 81 will be:
81 = 3 × 3 × 3 × 3
81 = 33 × 3
Hence, we need to divide 81 by 3 to get:
81/3 = 27 = 33
Question : By what number should we divide 135 to get a perfect cube?
(a) 3
(b) 5
(c) 7
(d) 9
Answer : (b)Show Answer :
Explanation: 135 = 3 x 3 x 3 x 5
We can see, 5 is the extra number which cannot be paired in a group of 3.
Hence, 135/5 = 27
Question : Cube root of 512 is:
(a) 4
(b) 6
(c) 8
(d) 12
Answer : (c)Show Answer :
Explanation: By prime factorisation we get:
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
3√512 = 2 × 2 × 2 = 8
Question : What should be divided by 53240 to make it a perfect cube?
(a) 5
(b) 10
(c) 15
(d) 20
Answer : (a)Show Answer :
Explanation: The prime factorisation of 53240
53240 = 2 × 2 × 2 × 11 × 11 × 11 × 5 = 23 × 113 × 5
Hence, we need to divide 53240 by 5
53240/5 = 10648 is a perfect cube.
Question : The value of 43√1000 is:
(a) 400
(b) 40
(c) 10
(d) 4
Answer : (b)Show Answer :
Explanation: 43√1000 = 43√(10×10×10) = 4 × 10 = 40
Question : A perfect cube does not end with _____ zeros.
(a) 1
(b) 2
(c) 3
(d) 4
Answer : (b)Show Answer :
Examples: 103 = 1000
203 = 8000
303 = 27000
Question : Cube root of 15625 is:
(a) 5
(b) 15
(c) 25
(d) 35
Answer : (c)Show Answer :
Explanation: 15625 = 5 x 5 x 5 x 5 x 5 x 5
3√15625 = 5 × 5 = 25
Question : Which of the following is not a perfect cube?
(a) 1
(b) 9
(c) 8
(d) 27
Answer : (b)Show Answer :
Question : The cube of 4 is _______________ .
(a) 12
(b) 8
(c) 4
(d) 64
Answer : (d)Show Answer :
Question : The value of 5³ is __________ .
(a) 125
(b) 15
(c) 10
(d) 75
Answer : (d)Show Answer :
Question : The cube of an even number is always ____________ .
(a) odd number
(b) even number
(c) prime number
(d) none of these
Answer : (b)Show Answer :
Question : The cube of an odd number is always __________ .
(a) odd number
(b) even number
(c) prime number
(d) none of these
Answer : (a)Show Answer :
Question : Each prime factor appears _________ times in its cube?
(a) 2
(b) 3
(c) 1
(d) 4
Answer : (b)Show Answer :
Question : Which of the following is Hardy-Ramanujan Number?
(a) 1724
(b)1725
(c) 1727
(d) 1729
Answer : (d)Show Answer :
Question : By which smallest natural number 392 must be multiplied so as to make the product a perfect cube?
(a) 2
(b) 14
(c) 7
(d) 49
Answer : (c)Show Answer :
Question : The smallest natural number by which 243 must be multiplied to make the product a perfect cube is __________ .
(a) 3
(b) 9
(c) 8
(d) 7
Answer : (a)Show Answer :
Question : The smallest natural number by which 704 must be divided to obtain a perfect cube is
(a) 22
(b) 12
(c) 11
(d) 13
Answer : (c)Show Answer :
Question : The smallest natural number by which 135 must be divided to obtain a perfect cube is
(a) 5
(b) 3
(c) 15
(d) 9
Answer : (a)Show Answer :
Question : Which of the following is not a perfect cube?
(a) 216
(b) 343
(c) 125
(d) 108
Answer : (d)Show Answer :
Question : The expansion of a³ is ___________ .
(a) 3 × a
(b) a+a+a
(c) 3 × 3 × 3
(d) a × a × a
Answer : (d)Show Answer :
Question : What will be the unit digit of the cube of a number ending with 2?
(a) 8
(b) 4
(c) 2
(d) 6
Answer : (a)Show Answer :
Question : What will be the unit digit of the cube of a number ending with 4?
(a) 4
(b) 6
(c) 2
(d) 8
Answer : (a)Show Answer :
Question : What will be the unit digit of the cube of a number ending with 6?
(a) 4
(b) 6
(c) 2
(d) 8
Answer : (b)Show Answer :
Question : A cuboid has dimensions 5cm , 2cm, 5cm .How many such cuboid will be needed to form a cube?
(a) 20
(b) 10
(c) 5
(d) 2
Answer : (a)Show Answer :
Question : How many cuboids of dimensions 15cm, 30cm ,15cm will be needed to form a cube?
(a) 15
(b) 4
(c) 30
(d) 5
Answer : (b)Show Answer :
Question : 729 is the value of _______________ .
(a) 8³
(b) 9³
(c) 6³
(d) 4³
Answer : (b)Show Answer :
Question : Which of the following is a perfect cube?
(a) 125
(b) 135
(c) 145
(d) 115
Answer : (a)Show Answer :
Question : What is the volume of a cube whose edge is 2cm?
(a) 8
(b) 6
(c) 10
(d) 4
Answer : (a)Show Answer :
Question : The symbol for cube root is __________ .
(a) √3
(b) ∛
(c) 3√3
(d) 2√3
Answer : (b)Show Answer :
Question : The cube root of 512 is ________ .
(a) 8
(b) 32
(c) 16
(d) 2
Answer : (a)Show Answer :
Question : The value of
(a) 8
(b) 7
(c) 6
(d) 3
Answer : (b)Show Answer :
Question : Which of the following is true for any natural number n?
(a) n²>n³
(b) n³>n²
(c) n²=n³
(d) none of these
Answer : (b)Show Answer :
Question : If the volume of a cube is 125 cm3 then what would be the length of its side?
(a) 25
(b) 5
(c) 4
(d) 15
Answer : (b)Show Answer :
Question : What will be the unit digit of the cube root of a number ends with 8?
(a) 2
(b) 8
(c) 4
(d) 6
Answer : (a)Show Answer :
Question : What will be the unit digit of the cube root of a number ends with 2?
(a) 2
(b) 8
(c) 4
(d) 6
Answer : (b)Show Answer :
Question : What will be the unit digit of the cube root of a number ends with 3?
(a) 3
(b) 7
(c) 5
(d) 2
Answer : (b)Show Answer :
Question : What will be the unit digit of the cube root of a number ends with 7?
(a) 3
(b) 7
(c) 6
(d) 5
Answer : (a)Show Answer :
Question : 9 is the cube root of __________ .
(a) 343
(b) 729
(c) 629
(d) 81
Answer : (b)Show Answer :
Question : The number of digits in the cube root of a 6-digit number is _______ .
(a) 3
(b) 2
(c) 4
(d) 6
Answer : (b)Show Answer :
Question : How many digits will be there in the cube root of 46656?
(a) 2
(b) 1
(c) 3
(d) 4
Answer : (a)Show Answer :
Question : How many digits will be there in the cube root of 512?
(a) 1
(b) 2
(c) 3
(d) 4
Answer : (a)Show Answer :
Question : What will be the unit digit of
(a) 5
(b) 0
(c) 3
(d) 4
Answer : (a)Show Answer :
Question : How many zeros will be there in the cube root of 27000?
(a) 3
(b) 0
(c) 1
(d) 2
Answer : (c)Show Answer :
Question : How many zeros will be there in the cube root of 800?
(a) 3
(b) 0
(c) 1
(d) cube root does not exist
Answer : (d)Show Answer :
Question : If 7³=343 , then
(a) 3
(b) 7
(c) 13
(d) 9
Answer : (b)Show Answer :
Question : If 8³ = 512 , then
(a) 3
(b) 7
(c) 13
(d) 9
Answer : (a)Show Answer :
Question : What will be the unit digit of
(a) 3
(b) 6
(c) 4
(d) 2
Answer : (b)Show Answer :
Question : What will be the unit digit of the cube root of a number ends with 8?
(a) 2
(b) 8
(c) 4
(d) 6
Answer :(a) 2Show Answer :
Question : Which of the following numbers is a cube number ?
(a) 1000
(b) 400
(c) 100
(d) 600.
Answer :(a) 1000Show Answer :
Question : The prime factorisation of 64 is:
(a) 2 x 2 x 2
(b) 4 x 4 x 4
(c) 8 x 8 x 8
(d) None of the above
Answer :(d) 4 x 4 x 4Show Answer :
Question : The cube of an even natural number is
(a) odd
(b) even
(c) may be even, may be odd
(d) prime number
Answer :(d) evenShow Answer :
Question : What is the cube of double of ‘a’?
(a) 16a³
(b) 2a
(c) 8a³
(d) 4a²
Answer :(c) 8a³Show Answer :
Question : The smallest natural number by which 704 must be divided to obtain a perfect cube is
(a) 22
(b) 12
(c) 11
(d) 13
Answer :(c) 11Show Answer :
Question : Which of the following numbers is not a perfect cube ?
(a) 1331
(b) 512
(c) 343
(d) 100.
Answer :(d) 100.Show Answer :
Question : By what number should 81 be divided to get a perfect cube?
(a) 3
(b) 6
(c) 7
(d) 9
Answer :(a) 3Show Answer :
Question : The ones digit of the cube of the number 512 is
(a) 2
(b) 4
(c) 6
(d) 8
Answer :(d) 8Show Answer :
Question : Each prime factor appears _ times in its cube?
(a) 2
(b) 3
(c) 1
(d) 4
Answer :(d) 3Show Answer :
Question : If volume of cube is 4913cm³ then length of side of cube is
(a) 16 cm
(b) 17 cm
(c) 18 cm
(d) 19 cm
Answer :(d) 17 cmShow Answer :
Question : The cube of an odd natural number is
(a) even
(b) odd
(c) may be even, may be odd
(d) prime number.
Answer :(d) oddShow Answer :
Question : By what number should we divide 135 to get a perfect cube?
(a) 3
(b) 5
(c) 7
(d) 9
Answer :(d) 5Show Answer :
Question : The volume of a cubical box is 343 cm³ which of the following is the side of the box?
(a) 5 cm
(b) 4 cm
(c) 6 cm
(d) 7 cm
Answer :(d) 7 cmShow Answer :
Question : The expansion of a³ is _.
(a) 3 × a
(b) a + a + a
(c) 3 × 3 × 3
(d) a × a × a
Answer :(d) a × a × aShow Answer :
Question : The value of 5³ is __.
(a) 125
(b) 15
(c) 10
(d) 75
Answer :(a) 125Show Answer :
Question : The one’s digit of the cube of the number 111 is
(a) 1
(b) 2
(c) 3
(d) 9.
Answer :(a) 1Show Answer :
Question : What should be divided by 53240 to make it a perfect cube?
(a) 5
(b) 10
(c) 15
(d) 20
Answer :(a) 5Show Answer :
Question : Find the smallest number by which the number 72 must be multiplied to obtained a perfect cube.
(a) 2
(b) 3
(c) 4
(d) 8
Answer :(d) 3Show Answer :
Question : The numbers 1, 8, 27… are __.
(a) negative numbers
(b) cube numbers
(c) square numbers
(d) none of these
Answer :(d) cube numbersShow Answer :
Question : Ones place digit in the cube of 5832 is __.
(a) 5
(b) 7
(c) 2
(d) 8
Answer :(d) 8Show Answer :
Question : The one’s digit of the cube of the number 123 is
(a) 3
(b) 6
(c) 9
(d) 7.
Answer :(d) 7.Show Answer :
Question : Cube root of 15625 is:
(a) 5
(b) 15
(c) 25
(d) 35
Answer :(c) 25Show Answer :
Question : Which of the following is a perfect cube?
(a) 10,000
(b) 243
(c) 343
(d) 270000
Answer :(c) 343Show Answer :
Question : Express 6³ as the sum of odd numbers.
(a) 31 + 33 + 35 + 37 + 39 + 41 + 43
(b) 31 + 33 + 35 + 37 + 39 + 41
(c) 31 + 33 + 35 + 37 + 39 + 41 + 43 + 45
(d) none of these
Answer :(d) 31 + 33 + 35 + 37 + 39 + 41Show Answer :
Question : The cube root of the 216 × (−32) × 54 is __
(a) -36
(b) -72
(c) -48
(d) none of these
Answer :(d) -72Show Answer :
Question : The one’s digit of the cube of the number 326 is
(a) 2
(b) 3
(c) 6
(d) 4.
Answer :(c) 6Show Answer :
Question : The cube of an odd number is always __ .
(a) odd number
(b) even number
(c) prime number
(d) none of these
Answer :(a) odd numberShow Answer :
Question : Find the cube root of 0.001331.
(a) 0.111
(b) 0.101
(c) 0.11
(d) none of these
Answer :(c) 0.11Show Answer :
Question :How many digits will be there in the cube root of 46656?
(a) 2
(b) 1
(c) 3
(d) 4
Answer : (a) 2Show Answer :
Question :Ones digit of cube of a number depends on the ________ of the number.
(a) tens digit
(b) ones digit
(c) hundred digit
(d) none of these
Answer : (b) ones digitShow Answer :
Question :What will be the unit digit of the cube root of a number ends with 8?
(a) 2
(b) 8
(c) 4
(d) 6
Answer : (a) 2Show Answer :
Question :The symbol for cube root is __________.
(a) √3
(b) ∛
(c) 2√3
(d) 3√3
Answer : (b) ∛Show Answer :
Question :The smallest natural number by which 704 must be divided to obtain a perfect cube is
(a) 22
(b) 12
(c) 11
(d) 13
Answer : (c) 11Show Answer :
Question :The numbers 1, 8, 27… are ______.
(a) negative numbers
(b) cube numbers
(c) square numbers
(d) none of these
Answer : (b) cube numbersShow Answer :
Question :If volume of cube is 4913cm³ then length of side of cube is
(a) 16 cm
(b) 17 cm
(c) 18 cm
(d) 19 cm
Answer : (b) 17 cmShow Answer :
Question :The square of a natural number subtracts from its cube comes 100. The number is __________.
(a) 2
(b) 3
(c) 5
(d) 1
Answer : (c) 5Show Answer :
Question :The value of 53 is __________.
(a) 125
(b) 15
(c) 10
(d) 75
Answer : (a) 125Show Answer :
Question :If (2744)
(a) 3
(b) 6
(c) 2
(d) 8
Answer : (b) 6Show Answer :
Question :Ones place digit in the cube of 5832 is ______.
(a) 5
(b) 7
(c) 2
(d) 8
Answer : (d) 8Show Answer :
Question :Find the cube root of 0.001331.
(a) 0.111
(b) 0.101
(c) 0.11
(d) none of these
Answer : (c) 0.11Show Answer :
Question :If (504 + p) is a perfect cube number, whose cube root is p, then p = ______.
(a) 6
(b) 4
(c) 2
(d) 8
Answer : (d) 8Show Answer :
Question :The cube root of the 216 × (−32) × 54 is ________
(a) -36
(b) -72
(c) -48
(d) none of these
Answer : (b) -72Show Answer :
Question :The cube of an odd number is always __________.
(a) odd number
(b) even number
(c) prime number
(d) none of these
Answer : (a) odd numberShow Answer :
Question :Express 63 as the sum of odd numbers.
(a) 31 + 33 + 35 + 37 + 39 + 41 + 43
(b) 31 + 33 + 35 + 37 + 39 + 41
(c) 31 + 33 + 35 + 37 + 39 + 41 + 43 + 45
(d) none of these
Answer : (b) 31 + 33 + 35 + 37 + 39 + 41Show Answer :
Question :The cube of 23 is ___________
(a) 2304
(b) 23
(c) 12167
(d) 529
Answer : (c) 12167Show Answer :
Question :What will be the unit digit of the cube of a number ending with 6?
(a) 4
(b) 6
(c) 2
(d) 8
Answer : (b) 6Show Answer :
Question :The expansion of a3 is ___________.
(a) 3 × a
(b) a + a + a
(c) 3 × 3 × 3
(d) a × a × a
Answer : (d) a × a × aShow Answer :
Question :A natural number is said to be a perfect cube, if it is the cube of some _________.
(a) natural number
(b) square number
(c) cube number
(d) cuboid number
Answer : (a) natural numberShow Answer :
Question :Each prime factor appears _________ times in its cube?
(a) 2
(b) 3
(c) 1
(d) 4
Answer : (b) 3Show Answer :
Question :What is the cube of double of ‘a’?
(a) 16a3
(b) 2a
(c) 8a3
(d) 4a2
Answer : (c) 8a3Show Answer :
Question : The one’s digit of the cube of 53 is:
(a) 9
(b) 3
(c) 7
(d) 1
Answer :CShow Answer :
Explanation: 533 = 53 x 53 x 53
33 = 3x3x3 = 27
Hence, at the unit place, we will get 7.
Recheck: 533 = 53 x 53 x 53 = 148877
Question : The prime factorisation of 64 is
A. 2 x 2 x 2
(b) 4 x 4 x 4
(c) 8 x 8 x 8
(d) None of the above
Answer : DShow Answer :
Explanation: 64 = 2 x 2 × 2 x 2 x 2 x 2 = 26
Question : Which of the following is not a perfect cube?
(a) 216
(b) 1000
(c) 243
(d) 1331
Answer :CShow Answer :
Explanation: 243 = 3 × 3 × 3 × 3 × 3 = 33 × 32
Question : By what number should 81 be divided to get a perfect cube?
(a) 3
(b) 6
(c) 7
(d) 9
Answer :AShow Answer :
Explanation: The prime factorisation of 81 will be:
81 = 3 × 3 × 3 × 3
81 = 33 × 3
Hence, we need to divide 81 by 3 to get:
81/3 = 27 = 33
Question : By what number should we divide 135 to get a perfect cube?
(a) 3
(b) 5
(c) 7
(d) 9
Answer : BShow Answer :
Explanation: 135 = 3 x 3 x 3 x 5
We can see, 5 is the extra number which cannot be paired in a group of 3.
Hence, 135/5 = 27
Question : Cube root of 512 is:
(a) 4
(b) 6
(c) 8
(d) 12
Answer :CShow Answer :
Explanation: By prime factorisation, we get:
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
3√512 = 2 × 2 × 2 = 8
Question : What should be divided by 53240 to make it a perfect cube?
(a) 5
(b) 10
(c) 15
(d) 20
Answer :AShow Answer :
Explanation: The prime factorisation of 53240
53240 = 2 × 2 × 2 × 11 × 11 × 11 × 5 = 23 × 113 × 5
Hence, we need to divide 53240 by 5
53240/5 = 10648 is a perfect cube.
Question : The value of 43√1000 is:
(a) 400
(b) 40
(c) 10
(d) 4
Answer :BShow Answer :
Explanation: 43√1000 = 43√(10×10×10) = 4 × 10 = 40
Question : A perfect cube of a number having 0 at its unit place, ends with _____ zeros.
(a) 1
(b) 2
(c) 3
(d) 4
Answer :CShow Answer :
Examples: 103 = 1000
203 = 8000
303 = 27000
Question : Cube root of 15625 is:
(a) 5
(b) 15
(c) 25
(d) 35
Answer :CShow Answer :
Explanation: 15625 = 5 x 5 x 5 x 5 x 5 x 5
3√15625 = 5 × 5 = 25
Question : Which of the following is a perfect cube?
(a)125
(b) 36
(c) 75
(d) 100
Answer : A. 125Show Answer :
Explanation:
125 = 5 × 5 × 5 = 5³
Question : What is the cube of 2a?
(a) 2a3
(b) 4a3
(c) 8a3
(d) 16a3
Answer : C. 8a3Show Answer :
Explanation:
(2a)3 = 2a x 2a x 2a
= (2 x 2 x 2) x (a x a x a)
= 8a3
Question : 1. The cube root of 13824 is __________.
(a) 36
(b) 25
(c) 24
(d) 16
Answer : C. 24Show Answer :
Explanation: Prime factorisation of 13824 is:
13824=2×2×2×2×2×2×2×2×2×3×3×3
13824=(2×2×2)×(2×2×2)×(2×2×2)×(3×3×3)
Taking cube root both the sides, we get;
(13824)⅓ = 2 x 2 x 2 x 3 = 24
Question : Which of these numbers is not a cube number?
(a) 10000
(b) 343
(c) 64
(d) 729
Answer : A. 10000Show Answer :
Explanation: By prime factorisation method.
10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5.
= 24 × 54 = 2³ × 2 × 5³ × 5
Thus, the factors cannot be cubed.
Question : 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
Answer : D. 5Show Answer :
Explanation: Square of 5 = 5 x 5 = 25
Cube of 5 = 5 x5x5 = 125
125 – 25 = 100
Question : 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
Answer : A. 3Show Answer :
Explanation: 243 x 3 = 729
Hence, by prime factorisation of 729 we get;
729 = 3 x 3 x 3 x 3 x 3 x 3
729 = 33 x 33
Taking cube root on both the sides, we get;
(729)⅓ = 3 x 3 = 9
Question : The one’s digit of the cube of the number 111 is:
(a) 1
(b) 2
(c) 3
(d) 9
Answer : A. 1Show Answer :
Explanation: The unit place of 111 has 1.
Cube of 1 = 13 = 1 x 1 x 1 = 1
Question : The cube of 23 is:
(a) 2304
(b) 12167
(c) 529
(d) 23
Answer : B. 12167Show Answer :
Explanation: Cube of 23 = 23 x 23 x 23 = 12167
Question : The one’s digit of the cube of the number 242 is
(a) 2
(b) 4
(c) 6
(d) 8
Answer : D. 8Show Answer :
Explanation: The unit digit of 242 is 2.
Cube of 2 = 2 x 2 x 2 = 8
Question : Find the smallest number by which the number 200 must be multiplied to obtain a perfect cube.
(a) 2
(b) 10
(c) 5
(d) 100
Answer : C. 5Show Answer :
Explanation: The prime factorisation of 200 gives:
200 = 2 × 2 × 2 × 5 × 5 = 2³ × 5 × 5
Now multiply by 5 on both sides.
200 x 5 = 2³ × 53
(1000)1/3 = 2 × 5 = 10