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Cubes and Cube Roots — Revision Notes

ICSE · Class 8 · Mathematics

Cubes and Cube Roots revision notes for ICSE Class 8 Mathematics: 4 topics in quick points. Part of the ICSE Class 8 Mathematics syllabus.

40 questions25 flashcards9 formulas & key relations5 concepts

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Key Topics to Revise

1

1. Cube of a Number

  • For any number m, m × m × m is called the cube of m or m cube and is written as m^3.
  • Cube of a positive number is positive.
  • Cube of a negative number is negative.
2

2. Perfect Cubes and Prime Factorisation

  • The cube of a number is called a perfect cube.
  • A number is a perfect cube if it can be expressed as the product of triplets of equal factors.
  • Prime factorisation helps check whether all factors can be arranged in groups of three.
3

3. Making a Number a Perfect Cube

  • Sometimes a number must be multiplied or divided to become a perfect cube.
  • 3087 = 3 × 3 × 7 × 7 × 7, so one more 3 is needed.
  • 3087 multiplied by 3 gives 21^3.
4

4. Cube Roots

  • The cube-root of a given number is the number whose cube is the given number.
  • If ∛x = y, then y^3 = x.
  • Cube-root of a positive number is positive.

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Full Notes

Key Concepts

For any number mThe cube of a numberA number is factored into primesIf one prime factor is leftThe cube

Frequently Asked Questions

What are the important topics in Cubes and Cube Roots for ICSE Class 8 Mathematics?
Key topics in Cubes and Cube Roots include Cube of a Number, Perfect Cubes and Prime Factorisation, Making a Number a Perfect Cube, Cube Roots. Study these first, then practise questions on each for Class 8 exams.
How should I revise Cubes and Cube Roots for Class 8 exams?
Learn the core ideas first, then work through the 40 practice questions on Cubes and Cube Roots. Revise 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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