A Square and A Cube
CBSE · Class 8 · Mathematics
Quick revision notes for A Square and A Cube — CBSE Class 8 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Perfect Squares and Square Numbers
- A square number is obtained by multiplying a number by itself: n × n = n²
- Perfect squares are squares of natural numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
- Perfect squares can only end with digits 0, 1, 4, 5, 6, or 9
Perfect Cubes and Cube Numbers
- A cube number is obtained by multiplying a number by itself three times: n × n × n = n³
- Perfect cubes are cubes of natural numbers: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000...
- Perfect cubes can end with any digit from 0 to 9
Properties and Patterns
- Perfect squares have odd number of factors, all others have even number of factors
- In Queen Ratnamanjuri's puzzle, only lockers with square numbers remain open
- Prime numbers have exactly 2 factors (1 and the number itself)
Finding Square Roots and Cube Roots
- Prime factorization method: group factors in pairs for square roots, triplets for cube roots
- Estimation method: find perfect squares/cubes closest to the given number
- Successive subtraction of odd numbers can determine if a number is a perfect square
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A Square and A Cube covers several key topics that are frequently asked in CBSE Class 8 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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