Class 8 Mathematics — Chapter 1: A Square and A Cube
72 practice questions · 24 Easy · 24 Medium · 24 Hard
Practise the most important Class 8 Mathematics questions from Chapter 1, "A Square and A Cube" — 72 NCERT-aligned multiple-choice questions with answers and explanations. The set is split into 24 Easy, 24 Medium and 24 Hard, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams.
"A Square and A Cube" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+4 correct, −1 wrong, 0 skipped), training the same negative-marking accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on A Square and A Cube, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 8 Mathematics mastery score. A sample question is shown below; sign in free to see its answer and practise all 72.
Key concepts: A Square and A Cube (Class 8 Mathematics)
This chapter builds squares and cubes and their inverses. A square number is n × n and a cube number is n × n × n; their reverses are square roots and cube roots. You learn to spot perfect squares and cubes from their factors, see the patterns hidden in them — odd-number sums, triangular numbers, sums of cubes — and meet the famous Hardy–Ramanujan number 1729.
- Square number
- A number got by multiplying a whole number by itself: n² = n × n. Examples are 1, 4, 9, 16, 25; the squares grow by successive odd numbers.
- Square root
- The reverse of squaring: √(n²) = n, the side of a square whose area is that number. √196 = 14 because 14 × 14 = 196.
- Perfect square
- A number that is the square of a whole number. A perfect square can only end in 0, 1, 4, 5, 6 or 9 — never in 2, 3, 7 or 8, which gives a fast reject test.
- Sum of consecutive odd numbers
- Adding the first n odd numbers always gives n²: 1 + 3 + 5 + … + (2n − 1) = n². So 1 + 3 + 5 + 7 = 16 = 4².
Try a sample question
One free sample from this chapter — sign in to check your answer and practise the rest.
Find the square root of 441.
Unlock the full chapter — free
See the answer and solution to this question, then practise all 72 questions (24 Easy · 24 Medium · 24 Hard) with timed scoring and instant feedback, plus the complete key-concept notes, formulas & exam tips. Sign in with Google — no card needed.
Start this chapter free →A Square and A Cube — FAQs
What are the key concepts in Class 8 Mathematics A Square and A Cube?+
This chapter builds squares and cubes and their inverses. A square number is n × n and a cube number is n × n × n; their reverses are square roots and cube roots. You learn to spot perfect squares and cubes from their factors, see the patterns hidden in them — odd-number sums, triangular numbers, sums of cubes — and meet the famous Hardy–Ramanujan number 1729. Key ideas include Square number, Square root, Perfect square, Sum of consecutive odd numbers.
What does Class 8 Mathematics Chapter 1 (A Square and A Cube) cover on XamBaaz?+
It covers 72 NCERT-aligned MCQs on "A Square and A Cube" — 24 Easy, 24 Medium and 24 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams.
Are these "A Square and A Cube" questions free to practise?+
Yes — sign in with Google to practise "A Square and A Cube" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "A Square and A Cube" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Are these "A Square and A Cube" MCQs available with answers?+
Yes. This page shows one sample question so you can see the format; sign in free with Google to reveal the correct option and a step-by-step "Why" explanation for it, then practise all 72 questions with instant scoring.
Is there negative marking in the "A Square and A Cube" quizzes?+
Yes — the timed quizzes use exam-grade marking: +4 for a correct answer, −1 for a wrong one and 0 for a skipped question, so you practise the same negative-marking discipline as CBSE Board exams.
Are these important questions for A Square and A Cube?+
The set is curated to the NCERT syllabus and weighted toward the question patterns that actually appear in CBSE Board exams, across Easy, Medium and Hard — so it doubles as an "important questions" revision list for "A Square and A Cube".