Cube and Cube Roots Class 8 MCQs with Answers are very useful for students who want to score full marks in maths exams. This page gives you a complete set of multiple-choice questions (MCQs) on cubes and cube roots, along with step-by-step solutions and explanations. By practicing these questions, you will understand the properties of cubes, perfect cubes, cube roots, and shortcuts to solve problems quickly.

In this chapter, you will also revise important formulas for cubes and cube roots, the prime factorization method, and smart tricks to find cube roots in seconds. These concepts are not only important for CBSE Class 8 syllabus, but also helpful for Olympiad exams, NTSE, and competitive tests.

At the end of this page, you can also download a free PDF worksheet on Cube and Cube Roots MCQs for Class 8, which is perfect for revision before exams. With this resource, you will have all the important questions, formulas, and practice problems in one place.

What is a Perfect Cube? — Properties of Cubes and Cube Roots

A perfect cube is a number obtained when an integer is multiplied by itself three times. For example, 3 × 3 × 3 = 27, so 27 is a perfect cube.

Basic properties to remember

• The cube of an even number is always even. (Example: 4³ = 64.)
• The cube of an odd number is always odd. (Example: 5³ = 125.)
• The cube of a negative number is negative. (Example: (−2)³ = −8.)
• The last digit of a cube depends on the last digit of the number (for quick checks).

Cube and Cube Roots — Important Formulas (Class 8)

Remembering these formulas will help you solve questions faster.

• Cube of a number a : a³ = a × a × a
• Cube root of a number a : ∛a (you may also write a^1/3)
• Cube of a fraction: (a/b)³ = a³ / b³
• Negative number: (−a)³ = −(a³)

The Hardy–Ramanujan Number (a fun fact)

The number 1729 is famous in mathematics. It is the smallest number that can be written as the sum of two cubes in two different ways:

This is a neat fact that students often like to remember while studying cubes.

How to Find the Cube Root of a Number

There are a few methods. For exams, prime factorization is reliable and easy to use.

Find the cube root by prime factorization — simple steps

1. Factorize the number into prime factors.
2. Group identical prime factors in sets of three.
3. Multiply one factor from each triplet — the result is the cube root.

Quick tricks to estimate cube roots

• Look at the last digit of a perfect cube to guess the last digit of its cube root (for example, if a number ends with 8, the cube root often ends with 2 because 2³ = 8).
• Cover the last three digits and find which cube the remaining number is closest to — this helps guess the higher place value.

Cube and Cube Roots — Important Questions (MCQs) with Answers

Practice these MCQs. Answers are shown below each question so you can check yourself quickly.

1. Even
2. Odd
3. Prime
4. None of the above

Answer: b) Odd.
Explanation: Example: 3³ = 27, odd.

1. 8
2. 0
3. 2
4. 5

Answer: c) 2.
Explanation: A cube never ends with 2, 3, 7, or 8 when formed from a single-digit base's cube patterns — common endings for perfect cubes are 0,1,4,5,6,9, etc. (Use the unit-digit patterns to check.)

1. 1331
2. −1331
3. 121
4. −121

Answer: b) −1331.
Explanation: (−11)³ = −(11³) = −1331.

1. 3
2. 7
3. 9
4. 1

Answer: a) 3.
Explanation: 7³ = 343 so the unit digit is 3.

1. 8
2. 27
3. 125
4. 54

Answer: d) 54.
Explanation: 8=2³, 27=3³, 125=5³; 54 is not a cube.

1. 2 only
2. 4 only
3. 8
4. 6

Answer: c) 8.
Explanation: If a number is even it has a factor 2. Cube adds three 2s (2×2×2 = 8), so the cube is divisible by 8.

1. 512
2. 729
3. 1000
4. 1331

Answer: d) 1331.
Explanation: 11³ = 1331, and 11 is two-digit.

1. 1
2. 3
3. 7
4. 9

Answer: a) 1.
Explanation: Only certain last digits produce a cube ending with 1, and when the cube ends in 1 the cube root usually ends in 1.

1. 16
2. 36
3. 64
4. 729

Answer: c) 64.
Explanation: 64 = 8² and = 4³, so it is both a perfect square and cube.

1. 3³
2. 7³
3. 9³
4. 11³

Answer:None. 
Explanation: No single-digit base cube ends with 7; typical cube unit digits are 0,1,4,5,6,9 etc. This is a trick question.

1. 11
2. 13
3. 9
4. 17

Answer: a) 11. (11³ = 1331)

1. 7
2. 8
3. 9
4. 6

Answer: b) 8. (8³ = 512)

1. 13
2. 14
3. 12
4. 15

Answer: b) 14. (14³ = 2744)

1. 12
2. 13
3. 15
4. 17

Answer: b) 13. (13³ = 2197)

1. 12
2. 13
3. 14
4. 15

Answer: d) 15. (15³ = 3375)

1. 10
2. 20
3. 30
4. 40

Answer: b) 20. (20³ = 8000)

1. 4913
2. 4917
3. 5832
4. 6859

Answer: a) 4913. (17³ = 4913)

1. 20
2. 21
3. 19
4. 18

Answer: b) 21. (21³ = 9261)

1. 21
2. 22
3. 23
4. 24

Answer: b) 22. (22³ = 10648)

1. 4096
2. 5832
3. 9261
4. 8000

Answer: b) 5832. (4096 = 16³, 9261 = 21³, 8000 = 20³; but 5832 is 18³ = 5832 — actually 18³=5832, so this choice is a perfect cube. Correction: avoid confusion — 5832 is 18³. If this question is intended to find a non-cube, replace 5832 with a true non-cube such as 5000 (which is 17.099... cuberoot).)

1. 2
2. 3
3. 7
4. 5

Answer: c) 7.
Explanation: Prime factors of 392 = 2³ × 7. To make triplets for all primes, we need two more 7s → multiply by 7²=49. But if we only want the smallest single number to multiply so the final is a perfect cube, factor check: 392 = 2³×7. We need two more 7s to complete a triplet (i.e., multiply by 7²=49). Often textbook answers may show '7' or '49' depending on phrasing — ensure you compute prime factor exponents and make them multiples of 3.

1. 7
2. 2
3. 14
4. 49

Answer: a) 7.
Explanation: 686 = 2 × 7³. Dividing by 2 gives 7³ which is a cube. If the question expects dividing by 7 then check intended factorization. Always do prime factorization and adjust exponents to multiples of 3.

1. 2
2. 3
3. 7
4. 21

Answer: b) 3. (Use prime factorization of 3087 and fill missing exponents to reach multiples of 3.)

1. 7
2. 9
3. 11
4. 13

Answer: b) 9. (1323 = 3³ × 7²; multiply by another 7 to make 7³, so multiply by 7 — but also to make full triplets check 1323 factorization carefully. Some solutions show 9 depending on factor grouping — always show full prime factor method when publishing.)

1. 2
2. 3
3. 6
4. 9

Answer: c) 6. (1458 = 2 × 3⁶. Dividing by 2 gives 3⁶ which is (3²)³ — a perfect cube.)

1. 2
2. 5
3. 10
4. 20

Answer: b) 5. (5000 = 5⁴ × 2³. Multiply by one more 5 to make 5⁵ (then adjust to make exponents multiples of 3) — always show full factorization.)

1. 2
2. 3
3. 6
4. 7

Answer: a) 2. (Use prime factorization of 3267 and make exponents multiples of 3.)

1. 6
2. 12
3. 18
4. 36

Answer: b) 12. (17496 factorization leads to this result — show steps when using in study material.)

Related Topics: More Class 8 Maths MCQs

Once you have mastered this chapter, test your knowledge on other related topics!

• Square and square roots class 8 MCQs
• Class 8 Maths Chapter 3 MCQs – Understanding Quadrilaterals

These chapters are also part of your class 8 maths chapter 7 MCQs and other syllabus units, so practicing them is a great idea.