A Square and a Cube is the first chapter of Class 8 Maths in Ganita Prakash Part 1. It introduces perfect squares, perfect cubes, square roots, cube roots, and number patterns that help students recognise relationships between numbers. Practising A Square and a Cube Class 8 Maths MCQs helps learners apply these concepts, improve calculation skills, and build a stronger foundation for more advanced topics.
This chapter-wise question set is useful for checking your understanding of square and cube numbers before school assessments. Try identifying number patterns and solving root-based questions to see which concepts need more revision. The questions follow the CBSE Board syllabus. For further practice, browse Class 8 Maths MCQs to explore other Mathematics chapters, or visit Class 8 MCQs for questions from different subjects. You can also find more practice material in the MCQs collection.
Topics Covered
The chapter A Square and a Cube builds the foundation of number patterns and mathematical calculations. Before attempting exams, students should revise these important concepts:
| Topic | Learning Outcome |
| Perfect Squares | Learn how to identify square numbers |
| Properties of Squares | Understand patterns of square numbers |
| Square Roots | Find the original number from a square |
| Perfect Cubes | Identify numbers formed by cubing |
| Cube Roots | Learn the reverse process of finding cubes |
| Prime Factorisation | Find squares and cubes using factors |
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MCQs for Chapter 1 with Answers and Explanations
Practice these Class 8 Maths Chapter 1 A Square and a Cube MCQs with answers and explanations to revise important concepts like perfect squares, perfect cubes, square roots, cube roots, and their properties. These questions will help you strengthen your understanding of the chapter, test your knowledge, and prepare more confidently for your CBSE Board exams.
Q1. How many numbers that are not perfect squares are present between (30^2) and (31^2)?
(a) 62
(b) 60
(c) 61
(d) 59
Answer: (b) 60
Q2. The square of a number having 2 at its unit place will always have which digit at the unit place?
(a) 6
(b) 8
(c) 4
(d) 2
Answer: (c) 4
Q3. Find the number of perfect squares between 16 and 81.
(a) 6
(b) 8
(c) 5
(d) 4
Answer: (d) 4
Q4. A six-digit number can have a cube root with a maximum of:
(a) 6 digits
(b) 3 digits
(c) 2 digits
(d) 1 digit
Answer: (c) 2 digits
Q5. What is the cube root of 8?
(a) 4
(b) 2
(c) 16
(d) 64
Answer: (b) 2
Q6. Identify the number which is not a perfect square.
(a) 961
(b) 468
(c) 1600
(d) 2500
Answer: (b) 468
Q7. Which of these numbers cannot have 4 as the unit digit after squaring?
(a) 52
(b) 68
(c) 34
(d) 102
Answer: (c) 34
Q8. The cube value of a number can be:
(a) only positive
(b) positive or negative
(c) only negative
(d) never zero
Answer: (b) positive or negative
Q9. If the last digit of a number is 3, the last digit of its cube will be:
(a) 9
(b) 3
(c) 7
(d) 1
Answer: (c) 7
Q10. The cube of a number ending with digit 7 always ends with:
(a) 7
(b) 9
(c) 5
(d) 3
Answer: (d) 3
Q11. Which of the following are factor pairs of 25?
(a) Only (5,5)
(b) Only (1,25)
(c) Both (1,25) and (5,5)
(d) (2,25)
Answer: (c) Both (1,25) and (5,5)
Q12. Select the number that cannot represent a perfect square.
(a) 529
(b) 198
(c) 841
(d) 625
Answer: (b) 198
Q13. The square of a number ending with digit 9 has the unit digit:
(a) 9
(b) 6
(c) 3
(d) 1
Answer: (d) 1
Q14. Which digit cannot appear at the unit place of any square number?
(a) 4
(b) 8
(c) 6
(d) 0
Answer: (b) 8
Q15. Choose the square of an even natural number.
(a) 625
(b) 169
(c) 144
(d) 441
Answer: (c) 144
Q16. How many natural numbers are present between (13^2) and (14^2)?
(a) 13
(b) 14
(c) 28
(d) 26
Answer: (d) 26
Q17. Find the value of
1 + 3 + 5 + 7 + 9 + 11 + 13.
(a) 52
(b) 49
(c) 41
(d) 36
Answer: (b) 49
Q18. Calculate the square root of 196.
(a) 15
(b) 12
(c) 14
(d) 11
Answer: (c) 14
Q19. Find the smallest square number exactly divisible by 2, 3, and 8.
(a) 576
(b) 64
(c) 144
(d) 1296
Answer: (c) 144
Q20. What is the value of (24^3)?
(a) 15625
(b) 13824
(c) 10648
(d) 12167
Answer: (b) 13824
Q21. Choose the perfect cube from the following numbers.
(a) 512
(b) 243
(c) 392
(d) 8640
Answer: (a) 512
Q22. Which number given below is not a perfect cube?
(a) 125
(b) 667
(c) 343
(d) 216
Answer: (b) 667
Q23. Identify the cube of an even natural number.
(a) 4913
(b) 3375
(c) 1728
(d) 1331
Answer: (c) 1728
Q24. What will be the unit digit in the cube of 23?
(a) 7
(b) 9
(c) 6
(d) 3
Answer: (a) 7
Q25. Find the cube root of 6859.
(a) 21
(b) 17
(c) 18
(d) 19
Answer: (d) 19
Q26. A perfect square number cannot have which digit at its end?
(a) 6
(b) 1
(c) 8
(d) 9
Answer: (c) 8
Q27. Calculate the cube of 4.
(a) 128
(b) 64
(c) 32
(d) 16
Answer: (b) 64
Q28. Find the square value of 25.
(a) 725
(b) 525
(c) 125
(d) 625
Answer: (d) 625
Q29. Finding the cube root is the opposite process of:
(a) Squaring
(b) Division
(c) Cubing
(d) Addition
Answer: (c) Cubing
Q30. The cube obtained from any even number is always:
(a) Odd
(b) Prime
(c) Negative
(d) Even
Answer: (d) Even
Benefits of Practicing A Square and a Cube MCQs
Solving A Square and A Cube MCQ Class 8 questions helps students revise the chapter quickly and understand important concepts clearly. MCQ practice improves:
- Speed and accuracy in calculations
- Understanding of square and cube patterns
- Exam preparation through objective questions
- Confidence in solving Maths problems
- Ability to avoid common calculation mistakes
Tips to Solve
Follow these simple tips while solving questions:
- Remember squares from 1 to 30
- Learn cubes from 1 to 20
- Check the unit digit before solving lengthy questions
- Use prime factorisation for perfect squares and cubes
- Practice different types of MCQs regularly
A strong understanding of squares and cubes will make upcoming Maths chapters easier.
