A Square and A Cube — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 1
9 timed quizzes · Easy, Medium and Hard · Updated
Jump to the 6 solved questions
Practise the most important Class 8 CBSE Mathematics questions from Chapter 1, "A Square and A Cube". You get 9 timed quizzes of NCERT-based MCQs, with answers and explanations. The questions are split into Easy, Medium and Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams get right.
To score well in "A Square and A Cube", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on A Square and A Cube, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 8 Mathematics mastery score. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.
A Square and A Cube — important questions & MCQs with answers (Class 8 Mathematics)
6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.
0 of 6 answered
- Q1 of 6Easy
What is the value of 12²?
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Answer: 144
Explanation: Squaring means multiplying the number by itself: 12×12 = 144. It is not 12×13 = 156, a neighbouring product easily mistaken for the square.
- Q2 of 6Easy
What is the square root of 16?
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Answer: 4
Explanation: Since 4×4 = 16, the square root of 16 is 4. It is not 8 (16 ÷ 2) — halving a number does not give its square root.
- Q3 of 6Medium
What is the value of 6³ (the cube of 6)?
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Answer: 216
Explanation: n³ means multiplying n by itself three times: 6×6×6 = 216. It is not 6×6×3 = 108 — the third factor must also be 6, not the exponent 3.
- Q4 of 6Medium
Find the cube root of 216.
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Answer: 6
Explanation: The cube root of 216 is the number that cubed gives 216: 6×6×6 = 216. It is not 7, since 7×7×7 = 343, not 216.
- Q5 of 6Hard
1729 is famous as the Hardy–Ramanujan number because it is the smallest number expressible as a sum of two cubes in two different ways. One way is 1³ + 12³. What is the other?
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Answer: 9³ + 10³
Explanation: 1729 = 1³ + 12³ = 1 + 1728, and also 9³ + 10³ = 729 + 1000 — the two different sum-of-two-cubes forms that make 1729 famous.
- Q6 of 6Hard
What is the units digit of 43²?
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Answer: 9
Explanation: The units digit of n² depends only on n's units digit: 3² = 9, so 43² ends in 9, not in 0, 1 or 4.
A Square and A Cube notes: key concepts (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.
- Difference of consecutive squares
- (n + 1)² − n² = 2n + 1, the next odd number. This is why squares step up by 3, 5, 7, 9, … as n grows.
- Cube number
- A number got by multiplying a whole number by itself three times: n³ = n × n × n. Examples are 1, 8, 27, 64, 125.
- Cube root
- The reverse of cubing: the cube root of n³ is n. The cube root of 343 is 7 because 7 × 7 × 7 = 343.
- Perfect cube by factors
- In the prime factorisation of a perfect cube every prime appears a number of times that is a multiple of 3, e.g. 216 = 2³ × 3³ = 6³.
- Numbers that are both
- A number that is both a perfect square and a perfect cube is a perfect sixth power; the first after 1 is 64 = 8² = 4³ = 2⁶.
- Triangular numbers
- The counts 1, 3, 6, 10, 15, … got by adding consecutive whole numbers; the nth one is n(n + 1)/2 and it fills a triangular pattern of dots.
- Sum of cubes
- The sum 1³ + 2³ + … + n³ equals the square of the nth triangular number, so it is always a perfect square: 1³ + 2³ + 3³ = 36 = 6².
- The number 1729
- The Hardy–Ramanujan number — the smallest number expressible as a sum of two cubes in two different ways: 1729 = 1³ + 12³ = 9³ + 10³.
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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, Difference of consecutive squares, Cube number.
What does Class 8 Mathematics Chapter 1 (A Square and A Cube) cover on XamBaaz?+
It has 9 timed quizzes of NCERT-based MCQs on "A Square and A Cube", at Easy, Medium and Hard levels, and you never get the same set twice. Every question has an instant explanation. They help you prepare 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. One year from the day you pay. You stay in Class 8 till 31 March; on 1 April your account moves up to Class 9 and the rest of your year carries over. No chapter is charged separately.
How should I revise "A Square and A Cube" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "A Square and A Cube" MCQs available with answers?+
Yes. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "A Square and A Cube" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from A Square and A Cube (Class 8 Mathematics)?+
The questions that matter most test Square number, Square root, Perfect square, Sum of consecutive odd numbers, Difference of consecutive squares, Cube number. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise this chapter as timed quizzes.
Is there an online quiz for A Square and A Cube?+
Yes — Class 8 Mathematics A Square and A Cube has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.
Are there question answers and extra questions for A Square and A Cube (Class 8 Mathematics)?+
Yes. This page has 6 solved questions on A Square and A Cube, each with the correct answer and a short explanation. Sign in to practise this chapter as timed quizzes.