Irrational Numbers class #9th maths ll Rationalisation chapter -01 Number system#class9maths

Genius Classes – Nasir Hussain: 📘 Number System – Class 9 Maths 🔹 Chapter: Irrational Numbers & Rationalisation 🧠 1. Number System Overview The number system is a way of representing numbers in different forms. It includes: Natural Numbers (1, 2, 3…) Whole Numbers (0, 1, 2…) Integers (…, -2, -1, 0, 1, 2…) Rational Numbers Irrational Numbers 🔹 2. Rational Numbers A number is called a rational number if it can be written in the form: ✅ Examples: 1/2, -3/4, 5, 0 (since 5 = 5/1) 📌 Properties: Decimal expansion is terminating or non-terminating recurring Example: 1/2 = 0.5 (terminating) 1/3 = 0.333... (recurring) 🔹 3. Irrational Numbers A number is called an irrational number if it cannot be written in the form p/q. ✅ Examples: √2, √3, π (pi) 📌 Properties: Decimal expansion is non-terminating and non-recurring Cannot be expressed as a fraction 💡 Example: 🔹 4. Rationalisation Rationalisation means removing the irrational number (root) from the denominator. ✏️ Case 1: Simple Denominator Multiply numerator and denominator by √2: ✏️ Case 2: Binomial Denominator Multiply by conjugate (a − √b): 📌 What is Conjugate? (a + √b) and (a − √b) are called conjugates 🔹 5. Important Results Product of two irrational numbers can be rational Example: √2 × √2 = 2 Sum of rational and irrational number is irrational Example: 2 + √3 🎯 Exam Tips Always check denominator before rationalisation Use conjugate carefully Practice different types of problems Remember decimal expansion rules 🏫 Genius Classes – Nasir Hussain ✔ Class 9th Maths Concept Clear ✔ CBSE & BSEB Board Preparation ✔ Zero to Advanced Level ✔ Chapter-wise Notes & Practice If you want, I can also: ✅ �⁠Convert this into a YouTube thumbnail/poster ✅ �⁠Make short notes PDF ✅ �⁠Create practice questions with solutions