Class 10 Mathematics Real Numbers – Revision Notes

Class 10 Mathematics Real Numbers – Revision Notes for Class 10 students, prepared by the teachers at Shubham Foundation Classes, Karnal. These revision notes follow the latest CBSE syllabus and NCERT textbook, and cover the points that are most often asked in school tests and board exams. Read the key points below, then download the complete 4-page PDF for free.

Key points: Real Numbers – Revision Notes

• Fundamental Theorem of Arithmetic: every composite number can be written as a product of primes in a unique way (apart from order).
• For any two positive integers a and b: HCF(a, b) × LCM(a, b) = a × b.
• √2, √3 and √5 are irrational; the sum or product of a non-zero rational and an irrational number is irrational.
• Proof that √p is irrational uses contradiction: assume √p = a/b in lowest terms and show p divides both a and b.

How to use these notes

1. Read the chapter once in your NCERT textbook.
2. Go through these revision notes and mark anything you find difficult.
3. Solve the textbook exercises, then revise from the notes again before your test.

Stuck on a question? Students of Shubham Foundation Classes can ask their teacher in class, or contact the institute.

Video lessons: Class 10 Mathematics

• Real Numbers – Complete Chapter in One Shot48:20