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Cubes and Cube Roots

ICSE · Class 8 · Mathematics

Complete topic list for Cubes and Cube Roots in ICSE Class 8 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

40 questions25 flashcards5 concepts

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4 Topics · ICSE Class 8 Mathematics

Topics in Cubes and Cube Roots

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.

Key Concepts

Central concept: Cubes and cube roots in number form, perfect cubes, factorisation method, and cube-root rules

Cube of a numberPerfect cubePrime factorisation methodSmallest multiplier or divisorCube-rootNegative cube-rootsCube-root of productsCube-root of fractions

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 Flowchart showing how cubing a negative number results in a negative answer through step-by-step multiplication, Distribution showing that most numbers are not perfect cubes, Decision flowchart for identifying perfect cubes using prime factorization. These are the concepts ICSE Class 8 examiners draw on most — study them first, then practise related questions.
How to score full marks in Cubes and Cube Roots — ICSE Class 8 Mathematics?
Understand the core concepts first, then work through the 40 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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