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A Square and A Cube

CBSE · Class 8 · Mathematics

Complete topic list for A Square and A Cube in CBSE Class 8 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

42 questions22 flashcards5 concepts

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4 Topics · CBSE Class 8 Mathematics

Topics in A Square and A Cube

1

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
2

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
3

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)
4

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

Key Concepts

Numbers obtained by multiplying a naturalThe inverse operation of squaringNumbers obtained by multiplying a naturalThe inverse operation of cubingA number is a perfect square

Frequently Asked Questions

What are the important topics in A Square and A Cube for CBSE Class 8 Mathematics?
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.
How to score full marks in A Square and A Cube — CBSE Class 8 Mathematics?
Understand the core concepts first, then work through the 42 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All 7 chapters — CBSE Class 8 Mathematics Syllabus

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