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Cubes and Cube Roots — Chapter Summary

ICSE · Class 8 · Mathematics

Summary of Cubes and Cube Roots for ICSE Class 8 Mathematics. Key concepts: For any number m, The cube of a number and A number is factored into.

40 questions25 flashcards9 formulas & key relations5 concepts

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Overview

Cubes and cube roots are built from repeated multiplication of the same number. A cube uses three equal factors, so 5 cubed means 5 × 5 × 5 = 125. A perfect cube is any number that can be written as the product of triplets of equal factors, such as 216 = 2 × 2 × 2 × 3 × 3 × 3. The cube-root of a num

Key Concepts

For any number m

For any number m, m × m × m is called the cube of m and is written as m^3. The cube of a positive number is positive, and the cube of a negative numbe

The cube of a number

The cube of a number is called a perfect cube. A number is a perfect cube if all its prime factors can be arranged in triplets of equal factors.

A number is factored into primes

A number is factored into primes. If every prime appears in groups of three, the number is a perfect cube. For example, 2744 = 2 × 2 × 2 × 7 × 7 × 7,

If one prime factor is left

If one prime factor is left ungrouped, multiply by the missing factor to complete a triplet. If one extra factor is present, divide by that factor to

The cube

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

Learning Objectives

  • Understand the meaning of cube and cube notation m^3.
  • Identify perfect cubes using triplets of equal factors.
  • Test whether a number is a perfect cube by prime factorisation.
  • Find the smallest number to multiply or divide so a number becomes a perfect cube.
  • Understand cube-root as the inverse of cubing.

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.

More resources for Cubes and Cube Roots

All ICSE Class 8 Mathematics Chapter Summary

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