Real Numbers — Chapter Summary
Gujarat Board · Class 10 · Mathematics
Summary of Real Numbers for Gujarat Board Class 10 Mathematics. Part of the Gujarat Board Class 10 Mathematics syllabus.
Interactive on Super Tutor
Studying Real Numbers? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for chapter summary and more.
Free trial, no card needed.
Learn better with visuals Super Tutor pairs illustrations like this with notes and quizzes for Real Numbers.
Overview
Real numbers form the foundation of higher mathematics and encompass all rational and irrational numbers. In this chapter, we explore the Fundamental Theorem of Arithmetic, which states that every composite number can be uniquely expressed as a product of prime numbers. We also learn how to prove th
Key Concepts
Every composite number can be expressed
Every composite number can be expressed as a product of prime numbers. For example, 32760 = 2³ × 3² × 5 × 7 × 13. This means we break down a composite
This theorem states that every composite
This theorem states that every composite number can be expressed as a product of primes in exactly one way (ignoring the order of factors). For instan
A number is irrational if it
A number is irrational if it cannot be written as p/q where p and q are integers and q ≠ 0. Examples include √2, √3, √5, π, and 0.101101110... (non-re
This is a logical technique where
This is a logical technique where we assume the opposite of what we want to prove, and then show this assumption leads to an impossibility or contradi
A prime number is a natural
A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself (like 2, 3, 5, 7, 11, 13, ...). Divisibility refers to wh
Learning Objectives
- Understand and apply the Fundamental Theorem of Arithmetic to factorize composite numbers
- Learn that prime factorization of any composite number is unique
- Prove that numbers like √2, √3, √5 are irrational using the Fundamental Theorem of Arithmetic
- Use the divisibility properties of integers to find HCF and GCD
- Develop logical reasoning skills through proof by contradiction
Frequently Asked Questions
What are the important topics in Real Numbers for Gujarat Board Class 10 Mathematics?
How should I revise Real Numbers for the Gujarat Board Class 10 board exam?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Real Numbers
For serious students
Get the full Real Numbers chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Gujarat Board Class 10 Mathematics. Free to start, no card needed.