A Square and A Cube — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 1
72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated
Practise the most important Class 8 CBSE Mathematics questions from Chapter 1, "A Square and A Cube". You get 9 timed quizzes made from 72 NCERT-based MCQs, with answers and explanations. The questions are split into 24 Easy, 24 Medium and 24 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. 14 sample questions are solved in full below, with 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)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
What is the value of 12²?
A.144✓ CorrectB.143C.156D.132Answer: A. 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.
- Q2Easy
What is the square root of 16?
A.5B.4✓ CorrectC.3D.8Answer: B. 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.
- Q3Easy
What is the value of 2³?
A.6B.10C.4D.8✓ CorrectAnswer: D. 8
Explanation: The exponent 3 means multiply the base 2 three times: 2×2×2 = 8. It is not 2×3 = 6 — the exponent counts factors, it does not multiply the base.
- Q4Easy
What is the cube root of 8?
A.3B.1C.4D.2✓ CorrectAnswer: D. 2
Explanation: The cube root is the number multiplied by itself three times to give the target: 2×2×2 = 8. It is not 3, since 3×3×3 = 27, not 8.
- Q5Easy
What is the value of 13²?
A.168B.182C.169✓ CorrectD.156Answer: C. 169
Explanation: Squaring means multiplying the number by itself: 13×13 = 169. It is not 13×14 = 182, a neighbouring product easily mistaken for the square.
- Q6Easy
What is the square root of 36?
A.7B.5C.18D.6✓ CorrectAnswer: D. 6
Explanation: Since 6×6 = 36, the square root of 36 is 6. It is not 18 (36 ÷ 2) — halving a number is not the same as taking its square root.
- Q7Medium
The sum of the first 5 odd natural numbers (1 + 3 + 5 + …) is:
A.24B.25✓ CorrectC.10D.30Answer: B. 25
Explanation: The sum of the first n odd numbers equals n²: for n = 5, that is 5×5 = 25. It is not 5×2 = 10, which just doubles the count instead of squaring it.
- Q8Medium
Find the square root of 441.
A.22B.20C.21✓ CorrectD.23Answer: C. 21
Explanation: Since 21×21 = 441, the square root of 441 is 21. It is not 20 — 20×20 = 400 falls short of 441.
- Q9Medium
What is the value of 6³ (the cube of 6)?
A.216✓ CorrectB.210C.217D.108Answer: A. 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.
- Q10Medium
Find the cube root of 216.
A.7B.5C.8D.6✓ CorrectAnswer: D. 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.
- Q11Medium
The numbers 1, 3, 6, 10, 15, … are called:
A.square numbersB.triangular numbers✓ CorrectC.cube numbersD.prime numbersAnswer: B. triangular numbers
Explanation: Each term adds the next natural number in turn (1, +2, +3, +4…), which is exactly how triangular numbers are built — not square numbers, whose gaps grow by odd numbers (1, +3, +5…) instead.
- Q12Hard
What is the units digit of 43²?
A.0B.1C.4D.9✓ CorrectAnswer: D. 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.
- Q13Hard
What is the smallest number by which 48 must be multiplied to make it a perfect square?
A.4B.3✓ CorrectC.5D.8Answer: B. 3
Explanation: 48 = 2⁴×3; the 3 has an unpaired power of 1, so multiplying by 3 gives 2⁴×3² = 144 = 12². Multiplying by 4 or 8 only changes the already-even power of 2.
- Q14Hard
What is the value of 1³ + 2³ + … + 3³?
A.36✓ CorrectB.35C.39D.18Answer: A. 36
Explanation: The sum 1³+2³+…+n³ equals (n(n+1)÷2)²: for n = 3, that is (3×4÷2)² = 6² = 36.
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.
- 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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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, Difference of consecutive squares, Cube number.
What does Class 8 Mathematics Chapter 1 (A Square and A Cube) cover on XamBaaz?+
It has 72 NCERT-based MCQs on "A Square and A Cube": 24 Easy, 24 Medium and 24 Hard. Together they make 9 timed quizzes, 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. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" 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 14 solved important MCQs with answers and explanations. Sign in to practise all 72 questions on the 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.