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Chapter 1: A Square and a Cube Notes

Home / Class Notes / class 8 / Mathematics / Chapter 1: A Square and a Cube
✓ Free notes class 8 Mathematics 1 study file

About these notes

Class 8 Mathematics A Square and a Cube notes on Merit Spring ROH provide concise formula lists, key diagrams and worked examples to speed up revision. Main sub-topics: definition and properties of squares and cubes, square roots and cube roots, factorisation formulas (a+b)², (a-b)², a³ ± b³, tests for perfect squares/cubes using prime factorisation, area of a square and volume of a cube, shortcut methods and practice tips. Designed for CBSE and Bihar Board students preparing for school exams, chapter test and board-pattern mock tests; use these notes for revision, practise MCQ and important questions and check question answer clarity.

Key points you will learn

  • Class 8 Mathematics A Square and a Cube notes: concise formulas, diagrams and worked examples
  • (a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b²
  • a³ + b³ = (a+b)(a² - ab + b²); a³ - b³ = (a-b)(a² + ab + b²)
  • Perfect square test: all prime exponents even; perfect cube test: all prime exponents multiples of 3
  • Volume of cube V = a³ and area of square A = side² (use x² notation)
  • Find square root/cube root by prime factorisation and short-division shortcuts
  • Identify last-digit patterns for squares and cubes to answer quick MCQ
  • Common exam tip: convert numbers into prime factors first to spot perfect squares/cubes quickly

What is inside this chapter

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A Square and a Cube - Chapter 1 Notes (Class 8 Maths)

Class 8 Maths A Square and a Cube - Chapter 1 handwritten-style revision notes for CBSE and Bihar Board students.

📥 Open notes

Questions students ask

What is in Class 8 Maths Chapter 1 A Square and a Cube notes?

The notes list the chapter's sub-topics and practice material: properties of squares and cubes, square roots and cube roots, factorisation formulas, prime-factor tests, area/volume applications, plus worked examples and diagrams for revision.

How to find square root and cube root quickly?

For perfect roots use prime factorisation: split into primes and check exponents (even for squares, multiples of 3 for cubes); for non-perfect roots apply estimation and short-division practice to improve speed.

Difference between square and cube?

A square is a number raised to power 2 (x²) and relates to the area of a square; a cube is a number raised to power 3 (x³) and relates to the volume of a cube; roots undo these operations.

How to use prime factorisation to test perfect square or cube?

Factor the number into primes and examine exponents: all even exponents mean a perfect square, all exponents divisible by 3 mean a perfect cube; e.g., 2³ × 3² × 5 is neither a perfect square nor a perfect cube.

Where to find Class 8 A Square and a Cube important questions and MCQ?

Find chapter notes on Merit Spring ROH and use the site’s chapter tests and board-pattern mock tests to practise MCQ and exam-style important questions and to check your answers.

More Mathematics chapters

Chapter 2: Power Play Chapter 3: A Story of Numbers Chapter 4: Quadrilaterals Chapter 5: Number Play Chapter 6: We Distribute Yet Things Multiply Chapter 7: Proportional Reasoning 1 All chapters →

class 8 — other subjects

ENGLISH Social Science Science