PROVE: √3 is an Irrational Number | Step-by-Step Detailed Explanation | Class 9/10/11/Other Exams
📌 Title: PROVE: √3 is an Irrational Number | Step-by-Step Detailed Explanation | Class 9/10/11/Competitive Exams --- Description: Welcome to [AKdesign]! In this video, we provide a detailed and easy-to-understand proof that √3 is an irrational number, using the method of contradiction. This topic is important for CBSE Class 9, Class 10, Class 11, and various competitive exams (like NTSE, Olympiads, JEE, and more). --- 🧠 What You'll Learn: ✔️ What are rational and irrational numbers ✔️ Assumption method (contradiction technique) ✔️ How to prove √3 is not a rational number ✔️ Use of prime factorization ✔️ Step-by-step breakdown of the logic --- 🔍 Keywords: Prove root 3 is irrational Root 3 irrational proof CBSE class 9 number system Proof by contradiction Irrational numbers explained Rational vs irrational Class 10 math important questions Root 3 proof class 9 Real numbers chapter explanation 📝 Full Proof Summary (In Brief): To prove √3 is irrational: 1. Assume √3 is a rational number. 2. Then √3 = p/q where p and q are co-prime integers and q ≠ 0. 3. Squaring both sides: ⇒ 3 = p²/q² ⇒ p² = 3q² 4. This implies p² is divisible by 3, hence p is divisible by 3. Let p = 3k for some integer k. 5. Substituting back: ⇒ (3k)² = 3q² ⇒ 9k² = 3q² ⇒ q² = 3k² ⇒ q is divisible by 3 6. So, both p and q are divisible by 3, which contradicts our assumption that p and q are co-prime. ✅ Hence, √3 cannot be expressed as a rational number. 👉 Therefore, √3 is irrational. 🎯 Who Should Watch This: Class 9 & 10 students (Number System Chapter) Class 11 math foundation Students preparing for NTSE, JEE, NDA, CUET, SSC Anyone interested in basic number theory ❤️ Support the Channel: 🔔 Subscribe for more educational content 👍 Like the video if it helped 💬 Comment your doubts or topics you want next 📤 Share this video with your friends --- 📬 Follow us: Instagram & Gmail: [Sisodiyayuvraj0] Website/Blog: [Officialaksingh.blogspot.com]
