Class 10 Maths Chapter 1: Real Numbers Full Concept & Solutions | Exercise 1.1 & 1.2 | CBSE / NCERT

Welcome to Dhanab online lecture! 🎓 In this video, we cover Class 10 Maths Chapter 1: Real Numbers in detail according to the latest CBSE / NCERT syllabus. Whether you are starting from scratch or revising for your upcoming board exams, this complete lecture breaks down key theorems, prime factorization, and step-by-step solutions to every exercise question. 📌 What You Will Learn in This Video: Introduction to Real Numbers: Rational, irrational, integers, and natural numbers overview. The Fundamental Theorem of Arithmetic: Prime factorization, finding HCF and LCM, and the relationship: {HCF}(a, b).× {LCM}(a, b) = a × b. Revisiting Irrational Numbers: Rigorous proofs by contradiction (proving √2, √3, √5 and composite terms like 3 + 2√5 are irrational). NCERT Exercise Solutions: Detailed explanations for Exercises 1.1 and 1.2. ⏱️ Timestamps & Chapter Markers (Note: The timestamps below follow the standard NCERT Chapter 1 sequence for your ~1 hr 32 min video. Adjust the minute marks slightly to align precisely with your exact cuts!) [0:44] – Exercise 1.1, Q1: Express each number as a product of its prime factors [18:28] – Exercise 1.1, Q2: Find the LCM and HCF of the following pairs of integers and verify that {LCM} × {HCF} = {Product of the two numbers} [29:48] - Divisibility rule of numbers 1. Divisibility rule of 2 [31:25] Divisibility rule of 3 [32:45] Divisibility rule of 4 [33:49] Divisibility rule of 5 [34:19] Divisibility rule of 6 [35:09] Divisibility rule of 7 [39:21] Divisibility rule of 8 [39:58] Divisibility rule of 9 [40:18] Divisibility rule of 10 [41:25] Divisibility rule of 11 [43:04] Divisibility rule of 12 [43:24] Divisibility rule of 13 [45:45] Divisibility rule of 14 [46:12] Divisibility rule of 15 [46:14] Divisibility rule of 16 [46:46] Divisibility rule of 17 [47:19] Divisibility rule of 18 [47:56] Divisibility rule of 19 [48:32] Divisibility rule of 20 [48:46] Divisibility rule of 21 [48:50] Divisibility rule of 22 [48:56] Divisibility rule of 23 [49:52] – Exercise 1.1, Q3: Find the LCM and HCF of the following integers by applying the prime factorisation method [55:51]] – Exercise 1.1, Q4: Given that {HCF}(306, 657) = 9, find {LCM}(306, 657) [1:00:21] – Exercise 1.1, Q5 & Q6: Check whether 6^n can end with the digit 0 & explain why 7 \times 11 \times 13 + 13 is a composite number [01:03:23] – Exercise 1.1, Q7: Word Problem – Circular path and finding the minimum time using LCM [01:06:11] – If p be a prime number and p divides any integer a² then p also divides a i.e. if p|a² then p|a [01:10:05] – Exercise 1.2, Q1: Prove that \sqrt{5} is irrational [01:18:54] – Exercise 1.2, Q2: Prove that 3 + 2\sqrt{5} is irrational [01:28:23] – Exercise 1.2, Q3: Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2 🔔 Don't Forget To: 👍 Like the video if this explanation helped you! 💬 Comment below if you have any questions or doubts. 🔴 Subscribe to Dhanab online lecture and turn on the bell icon 🔔 for upcoming chapters and complete Class 10 board exam prep! 🏷️ Tags & Hashtags: #Class10Maths #RealNumbers #NCERTClass10 #CBSEBoardExam #Class10Chapter1 #MathsClass10 #DhanabOnlineLecture