Real Numbers Class 10 | Full Chapter Revision | FTA, HCF & LCM, √2 √3 √5 Proofs | CBSE 2026-27

Revise the whole of CBSE Class 10 Maths Chapter 1, Real Numbers, on a whiteboard, as per the CBSE syllabus for 2026-27 and the NCERT textbook (Reprint 2026-27). Theory, theorems and proofs only, explained step by step: the Fundamental Theorem of Arithmetic (statement, what is given, what it concludes), why prime factorisation is unique, HCF and LCM by prime factorisation, why HCF × LCM = a × b is guaranteed only for two numbers, NCERT's formulas for three numbers, Theorem 1.2, proof by contradiction, and the full proofs that √2, √3 and √5 are irrational, plus how to prove that 3 + 2√5 is irrational. With verified shortcuts, memory aids, common misconceptions and links to later chapters. Not in the 2026-27 syllabus, so not covered: Euclid's division algorithm and decimal expansions of rational numbers. ⏱ Chapters 0:00 Introduction 0:39 Roadmap 1:27 Foundations: the number family 3:22 The Fundamental Theorem of Arithmetic 8:05 Why uniqueness matters 9:04 HCF and LCM by prime factorisation 10:30 HCF × LCM = a × b 11:50 Three numbers 14:25 Shortcuts and real-life meaning 15:34 Irrational numbers 16:32 Theorem 1.2 17:42 Proof by contradiction 18:33 √2 is irrational: the proof 19:47 √3 is irrational 20:50 √5 is irrational, and √p in general 22:11 Rational and irrational: the rules 23:02 Proving 3 + 2√5 is irrational 24:17 Misconceptions 25:24 How this chapter connects 26:41 Recap 27:27 Next video and contact ▶ Next in the series: Chapter 2, Polynomials. Learn with Guidepoint Academy: visit or call us. 📍 Office No. 203, Omran Tower, Al Qasimia, Sharjah, UAE 📞 Call: 056 690 0311 | 050 512 2641 #RealNumbers #Class10Maths #CBSE2027 #CBSEClass10 #NCERT #GuidepointAcademy #Sharjah