Important Questions: CBSE Class 8 Mathematics Chapter 6 Cubes and Cube Roots

CBSE Class 8 Mathematics Chapter 6 Cubes and Cube Roots covers three major topics: identifying perfect cubes through prime factorisation, finding cube roots by the prime factorisation method, and recognising cube root patterns. Analysis of question papers from 2022 to 2025 shows this chapter consistently carries 6-8 marks. The 2024 Term-2 paper included one 2-mark VSA on identifying perfect cubes and one 5-mark problem combining prime factorisation with the concept of smallest multiplier. The 2025 sample paper released by CBSE in October included a case-based question (4 marks) involving volume of a cube, showing the board's shift towards application-based assessment. Most schools allocate 8-10 periods to this chapter, and it appears in the syllabus immediately after Squares and Square Roots, building on those concepts. The chapter holds particular importance because cube and cube root concepts reappear in Class 9 (polynomials) and Class 10 (real numbers).

The CBSE board typically includes 1-2 questions of 1 mark each from this chapter in the objective or very short answer section. These test quick recall of perfect cube properties, cube patterns, and basic cube root calculations. The 2023 exam included an MCQ asking which of four numbers is a perfect cube. The 2025 sample paper had a fill-in-the-blank on the cube of 0.4. Speed and accuracy are crucial here because these questions take 30-45 seconds each. Students must memorise cubes of numbers 1 to 20 and recognise that perfect cubes end only in 0, 1, 4, 5, 6, or 9. Remember: a number ending in 2, 3, 7, or 8 can still be a perfect cube (8, 27, 343, 512), but recognition of patterns helps eliminate wrong MCQ options quickly.

Two-mark questions from Cubes and Cube Roots usually involve straightforward calculations or single-step reasoning. CBSE examiners look for clear method and accurate arithmetic. A common format is: 'Find the cube of [fraction or decimal]' or 'Is 1728 a perfect cube? Justify your answer.' The mark scheme awards 1 mark for correct method and 1 mark for accurate final answer. Students often lose the method mark by jumping directly to the answer without showing multiplication or factorisation steps. In the 2024 Delhi region paper, a 2-mark question asked students to find the cube of -12, and nearly 30 percent of students wrote 1728 instead of -1728, forgetting that the cube of a negative number is negative. Always write the sign explicitly.

Three-mark questions form the backbone of this chapter in CBSE exams. The most common question type asks: 'Find the smallest number by which [given number] must be multiplied (or divided) to make it a perfect cube.' This tests cube root by prime factorisation and understanding of triplet grouping. The mark distribution is typically: 1 mark for correct prime factorisation using factor tree or division method, 1 mark for grouping and identifying unpaired factors, and 1 mark for the final answer with reasoning. Students must show the factor tree or long division clearly. In the 2023 board exam, a 3-mark question on finding cube root of 10648 by prime factorisation was widely attempted, but many students made errors in the division steps. Write each division step on a new line and circle the final triplets for clarity.

From 2023 onwards, CBSE introduced case-based or integrated questions worth 4-5 marks that combine cubes with real-world contexts like volume of cubical containers, storage tanks, or gift boxes. A typical case-based question presents a paragraph about a water tank in the shape of a cube holding 13824 litres, then asks 3-4 sub-questions: (i) find the volume in cubic metres, (ii) find the edge of the tank using cube root, (iii) find the cost of painting all outer surfaces at ₹50 per square metre. The 2024 sample paper included such a question worth 5 marks. Each sub-part carries defined marks, and students must label their answers (i), (ii), (iii) clearly. Show all unit conversions explicitly: 1 litre = 1000 cm³, 1 m³ = 1000000 cm³. These questions test whether students can apply cube root by prime factorisation in practical scenarios, not just manipulate numbers abstractly.

Analysis of CBSE question papers from 2020 to 2025 reveals clear patterns in how examiners frame questions on Cubes and Cube Roots. Direct cube root calculations appear less frequently now; instead, CBSE prefers questions that test conceptual understanding and problem-solving. Common frameworks include: (a) 'Justify whether the given number is a perfect cube' — tests prime factorisation skill and triplet concept, (b) 'Find the smallest number by which [x] must be multiplied/divided' — the most repeated format, appearing in 4 out of 5 years, (c) Combination questions linking cubes to volume of cube, surface area, or even linking cube roots to finding dimensions, (d) Pattern recognition questions asking for ones digit of large cubes, and (e) Comparison questions: 'Which is greater: ∛512 or ∛729?' Since 2023, case-based formats present a real-world scenario (water tank, storage box, stacking cubes) followed by 3 sub-questions of increasing difficulty. Examiners deliberately choose numbers whose prime factorisation is non-trivial but manageable within 3-4 minutes, such as 2560, 8788, 13824.

Teachers and CBSE examiners report recurring errors that cost students 2-3 marks per paper. The single biggest mistake is incomplete prime factorisation: students stop too early or make arithmetic errors in division, leading to wrong grouping. For example, when factorising 2560, many write 2⁸×5 instead of 2⁹×5, losing all subsequent marks. Always verify your factorisation by multiplying back. The second major error is sign confusion: students write ∛(-64) = 8 instead of -4, forgetting that cube roots preserve sign. Third, in 'smallest number' questions, students confuse 'multiply' and 'divide', writing the reciprocal of the correct answer. Read the question twice and underline the key word. Fourth, many students apply square root methods to cube roots, trying to pair factors instead of grouping in triplets. Fifth, unit conversion errors plague case-based questions: writing 1 litre = 100 cm³ or forgetting to convert cm to m before calculating cost per square metre. Finally, students often omit the final statement, writing just '25' instead of 'The smallest number is 25', which can cost the concluding mark in a 3-mark question.

Cubes and Cube Roots is a highly scoring chapter if you follow systematic methods and avoid careless errors. First, memorise cubes of numbers 1 to 20 and recognise cubes of 25, 30, 40, 50 — this saves 30-45 seconds per question and helps in estimation. Second, master the prime factorisation method: use the division ladder (writing divisors on the left, quotients on the right) rather than factor trees, because it is faster and less error-prone for large numbers. Third, in 'smallest number' problems, write a clear table: Factor | Count | Needed for triplet | Shortfall or Excess. This structured approach ensures you never confuse multiply vs divide. Fourth, for case-based questions, read the entire case first, underline numerical data, then solve sub-parts in order — often (ii) depends on the answer from (i). Fifth, always write the final answer with units and a concluding sentence; CBSE mark schemes explicitly allocate 0.5 to 1 mark for proper statements. Sixth, practice estimation: ∛9000 is between 20 and 21 because 20³=8000 and 21³=9261; such checks catch factorisation errors. Finally, review your factorisation by multiplying factors back to the original number before moving to the next step.

The NCERT Class 8 Mathematics textbook for Chapter 6 contains carefully graded questions that mirror the exact difficulty level and format of CBSE board questions. The chapter has two exercises: Exercise 6.1 (9 questions on cubes and perfect cubes) and Exercise 6.2 (9 questions on cube roots). Questions you must solve include: Ex 6.1 Q5 (finding tens and ones digits of cubes), Ex 6.1 Q7 (smallest multiplier problems), Ex 6.2 Q2 (cube root by prime factorisation), and Ex 6.2 Q6 (cube root of fractions). The 2024 board exam directly adapted Ex 6.2 Q2(iii) asking for cube root of 10648. Additionally, the chapter contains 4 in-text 'Think, Discuss and Write' activities and 6 worked examples; these are gold mines for understanding examiner expectations. Example 5 in the NCERT textbook shows the method for finding cube root of a decimal, a format that appeared in the 2025 sample paper. Schools typically assign these as homework, but many students skip the 'Think, Discuss' portions — these often contain the seed ideas for case-based questions. Solve every NCERT question twice: once while learning the chapter, and once a week before exams for revision.

Many students in cities like Bengaluru, Pune, and even smaller towns struggle with Cubes and Cube Roots because prime factorisation feels mechanical until you understand WHY grouping in triplets works. Traditional tuitions often rush through this chapter in 4-5 classes, leaving gaps. CBSETUTOR.ai offers a 24×7 AI tutor that explains the logic behind each step, not just the procedure. Students can upload a photo of any question from this chapter — whether from school worksheets, NCERT exercises, or previous year papers — and receive step-by-step worked solutions within seconds, with each step explained in simple language. The platform's Class 8 Mathematics module includes 40+ practice questions on Cubes and Cube Roots, graded by difficulty and tagged by marks (1M, 2M, 3M, 5M), so students can practice exactly the question type they find difficult. For instance, if a student struggles with smallest-multiplier questions, they can filter for '3-mark smallest number problems' and get 10 similar questions with instant feedback. At a flat ₹999 per month for all subjects across Classes 6-12, it costs less than two hours of private tuition, yet provides unlimited doubt-solving. The 3-day free trial lets students test the AI tutor on 5-6 tricky cube root questions before committing, making it a risk-free investment in scoring those extra 6-8 marks from this chapter.