√5 + √3 is an irrational number || class X || chap 01 || Real numbers

Welcome to Deepak Kashyap’s Lecture! In today’s class, we will clearly and logically prove that √3 + √5 is an irrational number. This is one of the most important questions of the Real Numbers chapter (Class 9 & Class 10 NCERT), and it is frequently asked in board exams. 🔍 What You Will Learn in This Video ✔ What are rational and irrational numbers ✔ Why √3 and √5 themselves are irrational ✔ The method of contradiction (proof by contradiction) ✔ Step-by-step proof of the statement: 👉 √3 + √5 is an irrational number ✔ How to present this answer in board exam format ✔ Common mistakes students should avoid ✔ Important extra examples related to irrational numbers 🧠 Concept Explanation (Easy to Understand) In the Real Numbers chapter, we study how some numbers cannot be written in the form p/q. In this video, we assume √3 + √5 is rational and then show how it leads to a contradiction. This simple logic proves that the sum of two irrational numbers (√3 and √5) is not necessarily rational, but in this case, it is clearly irrational.