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Chapter Summary

Cubes and Cube Roots

ICSE · Class 8 · Mathematics

Summary of Cubes and Cube Roots for ICSE Class 8 Mathematics. Key concepts, important points, and chapter overview.

40 questions25 flashcards5 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 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.

More resources for Cubes and Cube Roots

All 25 chapters — ICSE Class 8 Mathematics Chapter Summary

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