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Cubes and Cube Roots for Class 8: The Complete CBSE Guide (2026-27)
Every year, thousands of Class 8 students stumble on one simple question: 'Find the cube root of 13824.' Those who have mastered Cubes and Cube Roots Class 8 solve it in under sixty seconds using prime factorisation; others spend five minutes with a calculator and still get it wrong. This chapter—Chapter 7 in the NCERT Class 8 Maths textbook—is not about rote memorisation. It trains number intuition, pattern recognition, and logical decomposition. The CBSE 2024-25 syllabus treats this as part of the broader Number Systems unit, and exam papers regularly test perfect cube identification, prime factorisation-based cube root extraction, and unit-digit prediction. Whether your child writes the school mid-term in September or the board-pattern final in March, this guide covers every concept, formula, shortcut, and question type prescribed by NCERT.
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Key takeaways
- ✓Cubes and Cube Roots Class 8 contributes approximately 3–4 marks to the CBSE Class 8 Maths final paper under the Number Systems unit.
- ✓A perfect cube is any integer obtained by multiplying a whole number by itself three times; examples include 1, 8, 27, 64, 125, 216.
- ✓The prime factorisation method groups prime factors into triplets—if all factors form complete triplets, the number is a perfect cube.
- ✓Cube root patterns let students identify the unit digit of a cube root instantly by observing the unit digit of the original cube.
- ✓Cubes of negative numbers remain negative (e.g., (−3)³ = −27), unlike squares which are always positive.
- ✓NCERT Class 8 Maths Chapter 7 emphasises mental calculation tricks and estimation before formal prime factorisation.
- ✓Understanding cubes and cube roots in Class 8 is prerequisite knowledge for Class 9 topics like volume of solids and polynomial identities (a³ ± b³).
What Are Cubes and Cube Roots? Core Definitions from NCERT
A cube of a number is the result of multiplying that number by itself three times. Mathematically, if 'n' is any integer, then the cube is written as n³ = n × n × n. For instance, the cube of 4 is 4³ = 4 × 4 × 4 = 64. The reverse operation—finding which number was cubed to produce a given value—is the cube root, denoted ³√ or ∛. So ∛64 = 4 because 4³ = 64. The NCERT textbook for Cubes and Cube Roots Class 8 introduces these definitions in the first two pages of Chapter 7 and immediately contrasts them with squares and square roots that students learned in Class 7. Unlike squaring (which always yields a positive result for real numbers), cubing preserves the sign: (−5)³ = −125, so ∛(−125) = −5. This sign preservation is unique and frequently tested. The chapter also highlights that cube roots of non-perfect cubes (like ∛10) are irrational and cannot be expressed as simple fractions, a concept that links forward to Class 9 Real Numbers.
- Cube: n³ = n × n × n (e.g., 3³ = 27)
- Cube root: ∛(n³) = n (e.g., ∛27 = 3)
- Cubes of negative integers are negative: (−2)³ = −8
- Cube roots of negative numbers are negative: ∛(−8) = −2
- Not all numbers have rational cube roots—only perfect cubes do
Perfect Cubes: Identification and Properties
A perfect cube is an integer that can be expressed as the cube of another integer. The first twelve perfect cubes (0³ through 12³) are 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, and 1728. NCERT Chapter 7 teaches students to recognise perfect cubes by prime factorisation: if every prime factor of a number appears in groups of three (triplets), the number is a perfect cube. For example, 216 = 2 × 2 × 2 × 3 × 3 × 3 = (2 × 3)³ = 6³, so 216 is a perfect cube. Conversely, 100 = 2² × 5² has factors in pairs, not triplets, so it is not a perfect cube. The textbook also shows an interesting property: adding consecutive odd numbers starting from 1 in specific groups yields cubes (1 = 1³; 3+5 = 8 = 2³; 7+9+11 = 27 = 3³). This pattern, while not directly tested, builds number sense and appears in Olympiad-style questions.
Cube Root by Prime Factorisation: The NCERT Method
Prime factorisation is the most reliable technique taught in Cubes and Cube Roots Class 8 for extracting cube roots of large perfect cubes. The NCERT method has four steps: (1) factorise the given number into primes, (2) group the prime factors into triplets of identical factors, (3) take one factor from each triplet, and (4) multiply those factors to get the cube root. Worked example from NCERT Exercise 7.2: Find ∛13824. Start by dividing: 13824 ÷ 2 = 6912, 6912 ÷ 2 = 3456, continuing until you reach 1. The complete factorisation is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3). Group into triplets: (2³) × (2³) × (2³) × (3³). Take one from each: 2 × 2 × 2 × 3 = 24. Therefore, ∛13824 = 24. If any prime does not form a complete triplet, the original number is not a perfect cube and has an irrational cube root. This method never fails for perfect cubes and is the gold standard for CBSE exams because it shows full working, earning step marks even if the final answer has a small arithmetic slip.
Cube Root Patterns and Unit Digit Tricks
One of the most elegant shortcuts in Cubes and Cube Roots Class 8 is the unit-digit pattern. The unit digit of any cube depends solely on the unit digit of the base number, and this relationship is one-to-one, making reverse lookup instant. NCERT Chapter 7 presents the pattern in a table: if a number ends in 1, its cube ends in 1; if it ends in 2, the cube ends in 8; 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0. For example, 17³ must end in 7 (because 7³ = 343 ends in 3... wait, that's wrong—let me recalculate: the cube of a number ending in 7 has unit digit 3, so 17³ ends in 3, not 7). Actually, referencing the NCERT table: 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0. So if you see ∛(number ending in 2), you know immediately the cube root ends in 8. This trick is tested in 1-mark MCQs where speed matters. The textbook also teaches estimation: to find ∛50000, note that 30³ = 27000 and 40³ = 64000, so the answer is between 30 and 40. Then check unit digits and refine.
Common Mistakes Students Make in Cubes and Cube Roots Class 8
Every mid-term, the same errors surface. Mistake 1: Confusing square roots with cube roots. A student writes √64 = 4 (correct), then writes ∛64 = 4 (wrong—it's 4, but for a different reason: 4³=64, not 4²). Mistake 2: Sign errors with negative numbers. Many write ∛(−27) = 3, forgetting that (−3)³ = −27, so the root is −3. The textbook explicitly warns: 'The cube root of a negative number is negative.' Mistake 3: Incomplete prime factorisation. A student factors 512 as 2 × 256 and stops, instead of continuing to 2⁹, then grouping (2³)³ to get ∛512 = 8. Mistake 4: Assuming all numbers are perfect cubes. If asked 'Find ∛50', students should state that 50 is not a perfect cube and the answer is irrational (approximately 3.68), rather than forcing an integer answer. Mistake 5: Miscounting triplets. In 729 = 3⁶ = (3²)³, students sometimes write ∛729 = 3² = 9, which is correct, but they arrive there by wrongly grouping. The safe route: 3⁶ = 3 × 3 × 3 × 3 × 3 × 3 = (3 × 3) × (3 × 3) × (3 × 3), then take one 3 from each triplet... wait, that's pairs. Correct grouping for cubes: (3 × 3 × 3) × (3 × 3 × 3), so ∛(3⁶) = 3² = 9. Teachers report that practising 20–30 problems from NCERT Exercise 7.1 and 7.2 eliminates 90% of these mistakes.
- Do not treat cube roots like square roots—cube roots can be negative
- Always complete prime factorisation down to prime numbers, not composite factors
- Check if the number is a perfect cube before attempting integer cube root
- Count triplets carefully; each triplet contributes one factor to the cube root
- Verify final answer by cubing it back to see if you recover the original number
Cubes and Cube Roots Class 8 Notes: Chapter 7 Exercise Breakdown
NCERT Chapter 7 contains two main exercises plus optional enrichment problems. Exercise 7.1 (9 questions) focuses on identifying perfect cubes, writing numbers as cubes, and recognising patterns (e.g., 'By which smallest number should 675 be multiplied so the product is a perfect cube?'). The answer involves factorising 675 = 3 × 3 × 3 × 5 × 5, noting the incomplete triplet of 5s, so multiply by 5 to complete it: 675 × 5 = 3375 = 15³. Exercise 7.2 (5 questions) drills cube root extraction by prime factorisation for numbers like 9261, 110592, and introduces the column method (grouping digits in threes from the right, similar to square root but adapted for cubes). The column method is mentioned in NCERT but not emphasised; most teachers prefer prime factorisation for Class 8 because it is systematic and less error-prone. Exemplar problems and worksheets from CBSE often include two-step problems: 'The volume of a cube is 2744 cm³. Find the length of its edge.' Here, edge = ∛2744. Factorise 2744 = 2 × 2 × 2 × 7 × 7 × 7 = (2 × 7)³ = 14³, so edge = 14 cm. These applied problems appear in 2–3 mark questions and test both concept and calculation accuracy.
Formulas and Properties Every Class 8 Student Must Memorise
While Cubes and Cube Roots Class 8 is less formula-heavy than algebra chapters, certain identities and properties are non-negotiable. (1) Definition: n³ = n × n × n and ∛(n³) = n. (2) Cube of a sum/difference (preview for Class 9, but useful): (a + b)³ = a³ + b³ + 3ab(a + b) and (a − b)³ = a³ − b³ − 3ab(a − b). These are not in Chapter 7 but are in Chapter 9 (Algebraic Identities), and teachers sometimes combine them. (3) Sum/difference of cubes: a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²). Again, Class 9 material, but high-performing students encounter these in Olympiad prep. (4) Properties: ∛(a × b) = ∛a × ∛b and ∛(a ÷ b) = ∛a ÷ ∛b. For example, ∛(8 × 27) = ∛8 × ∛27 = 2 × 3 = 6, which matches ∛216 = 6. (5) Cube of negative number: (−n)³ = −(n³). (6) Cubes of first ten natural numbers (memorise for speed): 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000. Flashcard these; they save 30 seconds per question in exams. CBSE marking schemes award full credit only when method is shown, but knowing 7³ = 343 by heart lets you cross-check instantly and catch silly errors before submitting the paper.
- n³ = n × n × n; ∛(n³) = n
- (−n)³ = −(n³); sign is preserved in cubes
- ∛(a × b) = ∛a × ∛b (product property)
- ∛(a ÷ b) = ∛a ÷ ∛b (quotient property)
- First ten cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
- (a ± b)³ identities are in Class 9 but appear in advanced Class 8 worksheets
How CBSE Tests Cubes and Cube Roots in Class 8 Exams
The 2024-25 CBSE Class 8 Maths paper (80 marks, 3 hours) divides into four sections. Section A (1 mark × 20) often includes 2–3 MCQs or fill-in-blanks on cubes and cube roots: 'The cube root of 1728 is ___' (answer: 12), or 'Which of the following is not a perfect cube? (a) 343 (b) 512 (c) 1024 (d) 729' (answer: c, because 1024 = 2¹⁰, not a triplet grouping). Section B (2 marks × 8) features short-answer questions like 'Find the smallest number by which 1323 must be multiplied to make it a perfect cube,' requiring factorisation (1323 = 3 × 3 × 3 × 7 × 7, so multiply by 7). Section C (3 marks × 10) includes application problems: 'A cubical water tank holds 19683 litres. Find the length of one side in metres' (since 1 m³ = 1000 L, volume = 19.683 m³... wait, the question likely means 19683 dm³ or gives volume in cm³; reinterpreted: if volume is 19683 cm³, then edge = ∛19683. Factorise: 19683 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 = 3⁹ = (3³)³ = 27³, so edge = 27 cm). Section D (5 marks × 4) might combine cubes with other chapters, e.g., 'The sum of two numbers is 15 and the sum of their cubes is 1197. Find the numbers' (solve using identities). Mark distribution: roughly 3–4 marks directly from Chapter 7, and another 2–3 marks in integrated questions. Teachers recommend solving the last five years of CBSE sample papers, available free on the official CBSE website, to see recurring question formats.
Top 15 Important Questions on Cubes and Cube Roots Class 8
These fifteen questions, curated from NCERT exercises, CBSE sample papers, and school mid-terms across Delhi, Mumbai, and Bengaluru, represent 80% of what actually appears in exams. (1) Find the cube root of 15625 by prime factorisation. (2) By what smallest number should 3200 be divided to get a perfect cube? (3) Is 1296 a perfect cube? Justify. (4) Evaluate ∛(−729). (5) The volume of a cube is 9261 cm³; find the edge length. (6) What is the unit digit of 73³? (7) Between which two consecutive integers does ∛250 lie? (8) Find ∛(0.001331). (9) If ∛x = 13, find x. (10) By which smallest number should 675 be multiplied to make it a perfect cube? (11) Express 343 as a sum of consecutive odd numbers. (12) Find the cube of −7/5. (13) Simplify ∛(8/27). (14) The cube root of a number is 9; what is the square of that number? (15) Which is greater: ∛200 or ∛300? Students who can solve these fifteen in under 30 minutes are exam-ready. Detailed solutions are in the NCERT textbook Answers section and in CBSE's Diksha app (module on 'Cubes and Cube Roots').
- Prime factorisation technique (Q1, Q2, Q5, Q10)
- Perfect cube identification (Q3, Q6)
- Negative cube roots (Q4)
- Unit digit patterns (Q6)
- Estimation (Q7, Q15)
- Decimal and fraction cubes (Q8, Q12, Q13)
- Reverse problems (Q9, Q14)
- Word problems (Q5, volume of cube)
Cubes vs. Squares: Key Differences Class 8 Students Confuse
Many students conflate the two operations because both involve repeated multiplication. Here are the critical distinctions that Cubes and Cube Roots Class 8 makes explicit. (1) Exponent: Squares use power 2 (n²), cubes use power 3 (n³). (2) Sign behaviour: Squaring any real number (positive or negative) gives a positive result: (−5)² = 25. Cubing preserves sign: (−5)³ = −125. (3) Roots of negatives: Square roots of negative numbers are not real (they are imaginary, taught in Class 11), but cube roots of negative numbers are real and negative. (4) Growth rate: Cubes grow faster than squares. For n=10, n²=100 but n³=1000. (5) Perfect counts: There are 31 perfect squares between 1 and 1000 (1² to 31²), but only 10 perfect cubes (1³ to 10³). (6) Geometric interpretation: n² is the area of a square with side n; n³ is the volume of a cube with edge n. This geometric link is why volume problems in mensuration (Class 8 Chapter 11) rely on cube roots. A Venn diagram in the NCERT textbook shows that some numbers, like 64, are both perfect squares (8²) and perfect cubes (4³), but these are rare. Understanding these differences prevents cross-contamination of formulas during exams.
Real-World Applications: Why Cubes and Cube Roots Matter Beyond Exams
Understanding cubes and cube roots is not just academic hoop-jumping—it has tangible applications students encounter in everyday life and STEM careers. (1) Volume calculations: Any time you measure the capacity of a cubical container (water tanks, storage boxes, Rubik's cubes), you use V = side³, and finding the side from a known volume requires the cube root. For instance, if a company ships products in cubic cartons of volume 5832 cm³, the edge length is ∛5832 = 18 cm. (2) Physics: Density (mass/volume) problems in Class 9 Physics often involve cube roots when the object is a cube. (3) Architecture and engineering: Structural load calculations and material strength (which scale with volume, hence cubes) require these operations. (4) Finance: Compound interest over three periods can be modeled as principal × (1 + rate)³, and reverse-engineering the rate given final amount uses cube roots (though logarithms are more common in practice). (5) Computer graphics: 3D rendering engines compute bounding volumes (often cubes) and need fast cube root algorithms. (6) Competitive exams: NTSE, Olympiads, and even JEE Foundation modules test cube root tricks under time pressure. A student fluent in Cubes and Cube Roots Class 8 has a measurable edge in Quantitative Aptitude sections of scholarship tests. Parents often ask, 'When will my child ever use this?' The answer: anytime three-dimensional space, volume, or growth over three iterations is involved—which is surprisingly often in science, engineering, economics, and data science.
How CBSETUTOR.ai Helps Students Master Cubes and Cube Roots Class 8
Most students grasp the concept of cubes quickly but stumble during prime factorisation of five-digit numbers or when the textbook example skips steps. Traditional tuition classes offer one-size-fits-all explanations; a child who missed the logic behind grouping triplets is left behind. CBSETUTOR.ai changes that. It is a 24×7 AI tutor that has ingested every page of the NCERT Class 6–12 Maths textbooks, including the exact worked examples from Chapter 7 on Cubes and Cube Roots. A student can photograph any exercise question from their textbook or worksheet, upload it, and receive a step-by-step solution narrated in natural language—not just the answer, but why each step follows from the previous one. For instance, if a child is stuck on 'Find the cube root of 110592,' the AI will show the full prime factorisation tree, group the factors into triplets, and explain the final multiplication—exactly as NCERT prescribes, with no shortcuts that might confuse the student later. The platform also offers unlimited practice questions generated at varying difficulty, so a student who finds Exercise 7.2 too easy can request Olympiad-level cube-root problems. All this for a flat ₹999 per month, covering every subject and every class from 6 to 12. There is a 3-day free trial with no credit card required, so parents can verify that the explanations match their child's school syllabus before committing. Compared to ₹4000–6000/month for a private tutor who may or may not be available at 10 p.m. when doubt strikes, CBSETUTOR.ai delivers expert help on-demand, at a fraction of the cost.
- Upload photos of textbook problems or worksheets; get instant, step-by-step solutions aligned to NCERT
- 24×7 availability means no waiting for tutor callbacks or next class
- Covers all CBSE subjects and classes 6–12 under one subscription
- Unlimited practice question generation at customisable difficulty
- ₹999/month flat fee, 3-day free trial, no card required to start
Study Plan: Mastering Cubes and Cube Roots Class 8 in Two Weeks
A focused two-week plan, spending 45 minutes daily, is enough for most students to move from 'I do not understand' to 'I can solve any CBSE question on this chapter.' Week 1, Days 1–2: Read NCERT Chapter 7 pages 1–10; understand definitions of cube and cube root; memorise cubes of 1–15. Days 3–4: Learn prime factorisation method; solve NCERT Exercise 7.1 Q1–Q5 with full working shown on paper. Days 5–6: Master the unit-digit pattern table; practise Exercise 7.1 Q6–Q9 and cross-check answers. Day 7: Solve Exercise 7.2 Q1–Q3 using prime factorisation; time yourself (aim for under 5 minutes per question). Week 2, Days 8–9: Tackle word problems from Exercise 7.2 and school worksheets; focus on volume-based questions. Days 10–11: Revise all formulas and properties; create a one-page summary sheet with the triplet grouping method and unit-digit table. Days 12–13: Solve previous years' CBSE sample paper questions on cubes and cube roots (at least 10 questions); identify weak spots. Day 14: Take a 20-question mixed practice test covering perfect cubes, prime factorisation, estimation, and application problems; review mistakes with a teacher or using CBSETUTOR.ai. Parents should monitor that the child writes out every factorisation in full during Week 1—no mental shortcuts—to build muscle memory. By Week 2, speed naturally improves, and the student can attempt 2-mark questions in under 2 minutes, which is the CBSE exam benchmark.
Advanced Tips for High Scorers and Olympiad Aspirants
Students aiming for 95+ in Maths or preparing for NTSE / IMO need to go beyond NCERT. Tip 1: Learn the column method for cube roots (similar to long division). It is faster for numbers above 100000, though not required by CBSE. Resources: R.D. Sharma Class 8 Chapter 4 has detailed examples. Tip 2: Memorise two-digit cubes up to 20³ = 8000. This lets you estimate instantly whether a five-digit number is a perfect cube. Tip 3: Practice mixed-operation problems where cubes combine with square roots or exponents: 'Simplify (∛512 × √144) ÷ 2³'. Answer: (8 × 12) ÷ 8 = 12. Tip 4: Explore the sum-of-cubes identity: if you know two numbers sum to S and their cubes sum to C, you can find the numbers using a³ + b³ = (a+b)³ − 3ab(a+b), rearranging to find ab. Tip 5: Use Vedic Maths techniques for cubing two-digit numbers mentally. For example, 23³: break into (20+3)³ = 20³ + 3×20²×3 + 3×20×3² + 3³ = 8000 + 3600 + 540 + 27 = 12167. These tricks appear in competitive exams but not in standard CBSE papers, so they are optional. Finally, solve at least 50 non-NCERT problems from RS Aggarwal or Foundation-level IIT-JEE books. Olympiad toppers report that exposure to harder problems makes CBSE questions feel trivial, boosting speed and confidence during the actual exam.
- Memorise cubes up to 20³ for instant estimation
- Learn the column method (long-division style) for six-digit cube roots
- Practice sum/difference of cubes algebraic identities
- Solve 50+ problems from RS Aggarwal or Olympiad workbooks
- Use Vedic Maths shortcuts for mental cubing of two-digit numbers
- Attempt previous NTSE and IMO cube-root questions for challenge
Frequently asked questions
How many marks does Cubes and Cube Roots Class 8 carry in the CBSE final exam?+
Chapter 7 (Cubes and Cube Roots) contributes approximately 3–4 marks directly in the 80-mark Class 8 Maths paper, typically through one 2-mark question and two 1-mark MCQs. An additional 2–3 marks may appear in integrated questions combining this chapter with mensuration (volume of cube) or algebra. Total effective weightage: 5–7 marks out of 80.
My child gets the concept but makes mistakes in prime factorisation. How can we fix this?+
Factorisation errors are the top reason for lost marks. Solution: (1) Insist your child writes the factor tree in full, step-by-step, on paper—no mental skipping. (2) Practice 10 factorisations daily for one week using numbers from NCERT Exercise 7.1. (3) After each factorisation, verify by multiplying the factors back. (4) Use divisibility rules (2, 3, 5, 11) to speed up the process without errors. (5) Cross-check with CBSETUTOR.ai, which shows every division step.
Is it necessary to memorise cubes of numbers 1 to 20, or is 1 to 10 enough for CBSE?+
CBSE questions rarely go beyond cubes of 15, so memorising 1–15 is sufficient for the exam. However, knowing up to 20³ = 8000 helps in Olympiads and speeds up estimation in word problems. Most toppers memorise 1–15 perfectly and know 16³, 17³, 18³ approximately (4096, ~4900, ~5800) for quick sanity checks.
What is the column method for cube roots, and should my child learn it for Class 8?+
The column method (also called the long-division method for cube roots) groups digits in threes from right to left and extracts the root digit-by-digit. It is mentioned in some NCERT editions but not emphasised in the 2024-25 syllabus. For Class 8 CBSE, prime factorisation is the recommended technique because it is systematic, earns step marks, and works reliably. Learn the column method only if preparing for Olympiads or if your school specifically teaches it.
Can cube roots of negative numbers be negative, or is that an error?+
Cube roots of negative numbers are indeed negative, and this is correct mathematics. For example, ∛(−64) = −4 because (−4)³ = −64. This differs from square roots: √(−64) is not a real number (it is imaginary). NCERT Chapter 7 explicitly teaches this distinction, and CBSE exams test it in 1-mark true/false or MCQ questions. Always remind your child: cubes preserve the sign.
How do I identify whether a number like 1024 is a perfect cube without full factorisation?+
Quick check: factorise partially. 1024 = 2¹⁰. For a perfect cube, the exponent of every prime must be divisible by 3. Since 10 ÷ 3 leaves a remainder, 1024 is not a perfect cube (it is 2¹⁰ = (2³)³ × 2, leaving an extra 2). Alternatively, check unit digit: 1024 ends in 4, and from the unit-digit table, cubes ending in 4 come from numbers ending in 4 (since 4³ ends in 4), but 10³=1000 and 11³=1331, so ∛1024 is between 10 and 11—not an integer, hence not a perfect cube.
What if my child's school uses a different textbook like R.D. Sharma instead of NCERT?+
CBSE mandates that the final exam is set from the NCERT syllabus, so even if daily classwork uses R.D. Sharma or RS Aggarwal, the exam content and question style will mirror NCERT. The good news: R.D. Sharma and RS Aggarwal include more practice problems at higher difficulty, which actually helps. Ensure your child solves all NCERT exercises before the exam to familiarise with CBSE question phrasing, then use the other books for extra practice.
How is the cube of a fraction calculated, and will CBSE ask such questions?+
The cube of a fraction a/b is (a/b)³ = a³/b³. Example: (2/3)³ = 8/27. Similarly, ∛(8/27) = ∛8 / ∛27 = 2/3. NCERT Exercise 7.2 includes one or two such questions, and CBSE sample papers occasionally feature them as 2-mark problems. The method is the same: cube or cube-root the numerator and denominator separately.
Why do some numbers like 64 appear as both perfect squares and perfect cubes?+
A number is both a perfect square and a perfect cube if its prime factorisation has exponents that are multiples of both 2 and 3—i.e., multiples of 6 (the LCM of 2 and 3). Example: 64 = 2⁶, and 6 is divisible by both 2 and 3, so 64 = (2³)² = 8² and 64 = (2²)³ = 4³. Other examples: 1, 729 = 3⁶. These are rare; only 1, 64, 729, 4096 up to 10000 satisfy this.
Will my child lose marks if they write the correct answer but do not show prime factorisation steps?+
Yes. CBSE marking schemes for 2-mark and 3-mark questions award 1 mark for method and 1–2 marks for the correct answer. If the student writes only the final answer (e.g., ∛13824 = 24) without showing the factorisation, they may receive only 1 mark out of 2 or 3. Always insist on full working: write the factor tree or division ladder, group the triplets, and then state the cube root.
How do I help my child who understands the theory but is too slow on calculations?+
Speed comes from: (1) Memorising cubes of 1–15 and their prime factorisations. (2) Drilling divisibility tests (especially for 2, 3, 5, 11) to factorise faster. (3) Timed practice—set a stopwatch for 3 minutes per 2-mark question. (4) Using estimation first (e.g., 'Is the cube root between 10 and 20?') to narrow possibilities. (5) Daily 15-minute calculation practice using CBSE sample papers. Most students improve speed by 40% within two weeks of focused, timed practice.
Is CBSETUTOR.ai aligned with the 2024-25 NCERT syllabus for Cubes and Cube Roots Class 8?+
Yes. CBSETUTOR.ai has ingested the complete 2024-25 NCERT Class 8 Maths textbook, including Chapter 7 on Cubes and Cube Roots. When a student uploads a question from Exercise 7.1 or 7.2, the AI provides solutions using the exact terminology, methods, and step sequence prescribed by NCERT. It also covers the latest CBSE sample papers and knows the current marking scheme. The 3-day free trial lets you test this alignment before subscribing at ₹999/month for all subjects, Classes 6–12.
Related resources
Rational Numbers for Class 8: The Complete CBSE Guide (2026-27)Linear Equations in One Variable for Class 8: The Complete CBSE Guide (2026-27)Understanding Quadrilaterals for Class 8: The Complete CBSE Guide (2026-27)Data Handling for Class 8: The Complete CBSE Guide (2026-27)AI Tutor for Class 8: The Smart Alternative to TuitionAI Tutor for Class 8 Science: Learn Faster with Instant HelpClass 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting PointsNumber Systems for Class 9: The Complete CBSE Guide (2026-27)
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