Back to Maths on Exam Trends
Real Numbers
Medium trendapprox. 6 marksSections A/B/C — a 1-mark FTA or HCF–LCM MCQ/VSA plus one short-answer irrationality proof (≈6 marks in all).
CBSE 2027 — dates, rules and official papers →Ask the tutor1In an irrationality proof, always open with "assume √2 = a/b where a and b are coprime integers, b ≠ 0" — the coprime assumption is a marked step, and skipping it costs method marks even when the contradiction is reached.
Notesformulae · proofs · mind-map — one view
Learn the 4 conceptsteach yourself first, then practise each
Fundamental Theorem of Arithmetic (every composite = a unique product of primes)1–2 marks Visual
Express any composite as primes and justify why its HCF/LCM factorisation is unique.
HCF & LCM by prime factorisation (HCF = product of smallest common prime powers; LCM = greatest powers)2–3 marks Visual
Read HCF and LCM straight off the prime factorisations of the numbers.
HCF × LCM = product of the two numbers1–3 marks Visual
Recover the fourth quantity when the other three are given.
Irrationality of √2, √3, √5 by contradiction2–3 marks
Prove a surd is irrational using the coprime assumption and FTA.
When you’re ready — practise or test the whole topic