6. Cubes and Cube Roots

The chapter explores the concept of cubes and cube roots, highlighting their mathematical significance and interesting patterns. It emphasizes the relationship between cubes and their prime factors, and introduces the Hardy-Ramanujan numbers, known for being expressible as the sum of two cubes in two different ways. The chapter also covers methods for determining perfect cubes and their roots through prime factorization and provides numerous exercises to reinforce understanding.

Sections

  • 6

    Cubes And Cube Roots

    This section covers the concepts of cubes, cube roots, and their mathematical significance, focusing on Hardy-Ramanujan numbers and various patterns related to cubes.

    Learning Practice

  • 6.1

    Introduction

    The section introduces S. Ramanujan and his fascination with numbers, specifically highlighting the special characteristics of the number 1729.

    Learning Practice

  • 6.2

    Cubes

    This section introduces the concept of cubes, perfect cubes, and the fascinating properties of numbers expressed as sums of cubes.

    Learning Practice

  • 6.2.1

    Some Interesting Patterns

    This section explores interesting patterns found in the sum of consecutive odd numbers and their relationship to perfect cubes.

    Learning Practice

  • 6.2.2

    Smallest Multiple That Is A Perfect Cube

    This section explores the concept of perfect cubes and how to determine the smallest multiple of a number that can become a perfect cube.

    Learning Practice

  • 6.3

    Cube Roots

    This section focuses on understanding cube roots, the inverse operations of cubing numbers.

    Learning Practice

  • 6.3.1

    Cube Root Through Prime Factorisation Method

    This section introduces finding cube roots using the prime factorization method, elaborating on how to simplify cube roots by identifying prime factors.

    Learning Practice

  • 6.4

    What Have We Discussed?

    This section covers the concept of cube roots, illustrating their definition and the process to find them through prime factorization.

    Learning Practice

References

NCERT Study Material

Class Notes

Memorization

What we have learnt

  • Numbers like 1729, 4104, 13...
  • Numbers obtained when a num...
  • If in the prime factorisati...

Final Test

Revision Tests

Chapter FAQs