CBSE 10 Mathematics | 1. REAL NUMBERS by Pavan | Learn Smarter
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Engineering Courses
Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Certifications
Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

1. REAL NUMBERS

1. REAL NUMBERS

This chapter explores real numbers, focusing on the Fundamental Theorem of Arithmetic and its implications. It establishes that every composite number can be uniquely factored into prime numbers and discusses various applications of this theorem, including the proof of the irrationality of certain numbers. The chapter concludes with exercises and activities designed to reinforce understanding of these concepts.

5 sections

Enroll to start learning

You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

Navigate through the learning materials and practice exercises.

  1. 1
    Real Numbers
    Learn Practice

    This section explores fundamental concepts related to real numbers, focusing...

  2. 1.1
    Introduction
    Learn Practice

    This section introduces the fundamental concepts of real numbers, focusing...

  3. 1.2
    The Fundamental Theorem Of Arithmetic
    Learn Practice

    The Fundamental Theorem of Arithmetic states that every composite number can...

  4. 1.3
    Revisiting Irrational Numbers
    Learn Practice

    This section discusses the nature of irrational numbers, their properties,...

  5. 1.4
    Summary
    Learn Practice

    This section summarizes the key concepts related to the Fundamental Theorem...

What we have learnt

  • The Fundamental Theorem of Arithmetic states that every composite number can be expressed as a product of primes uniquely, apart from the order of factors.
  • If a prime number divides the square of an integer, it also divides the integer itself.
  • The chapter provides proofs that certain numbers, such as 2 and 3, are irrational.

Key Concepts

Fundamental Theorem of Arithmetic
Every composite number can be expressed as a product of primes, and this factorization is unique, except for the order of the factors.
Irrational Numbers
Numbers that cannot be expressed as a fraction of two integers, such as the square roots of prime numbers.
Highest Common Factor (HCF)
The largest positive integer that divides each of the given integers without leaving a remainder.
Lowest Common Multiple (LCM)
The smallest positive integer that is divisible by each of the given integers.

Additional Learning Materials

Supplementary resources to enhance your learning experience.

Study Material

NCERT Study Material