RD Sharma Solutions Class 9 Maths Chapter 3 Rationalisation
By Swati Singh
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Updated on 4 Apr 2025, 17:37 IST
RD Sharma Solutions for Class 9 Maths Chapter 3 – Rationalisation is an important chapter for Class 9 students. In this chapter, students will learn about algebraic identities and how to rationalise the denominator of a fraction. Rationalisation is the process of removing square roots or other radicals from the denominator of a fraction. In this chapter, students will also learn how to simplify algebraic expressions using these identities. It’s a good idea for students to memorise the identities before attempting any rationalisation problems.
RD Sharma Solutions are helpful for students to score well in their exams. These solutions are created by experts at IL and explain the complete method for solving each problem. To do well in exams, students can download the PDF of RD Sharma Solutions for Class 9 Maths Chapter 3 from the link below.
RD Sharma Solutions for Class 9 Maths Chapter 3 Rationalisation - Download PDF
RD Sharma Class 9 Chapter Chapter 3 Rationalisation PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 9 Chapter Chapter 3 Rationalisation PDF.
RD Sharma Solutions for Class 9 Maths Question with Answer Exercise wise
Exercise 3.1 – Simplifying Expressions Involving Surds
Q1. Simplify: √2 × √8
A: √2 × √8 = √(2×8) = √16 = 4
Q2. Simplify: √3 × √12
A: √(3×12) = √36 = 6
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Q3. Simplify: (√5)²
A: (√5)² = 5
Q4. Express √18 in simplest form
A: √18 = √(9×2) = 3√2
Q5. Express √50 in simplest form
A: √50 = √(25×2) = 5√2
Exercise 3.2 – Rationalising the Denominator (Basic)
Q1. Rationalise: 1/√2
A: Multiply numerator & denominator by √2
⇒ 1/√2 × √2/√2 = √2/2
Q2. Rationalise: 1/√3
A: = √3/3
Q3. Rationalise: 1/(2√5)
A: = √5 / (2×5) = √5/10
Q4. Rationalise: 3/√7
A: = 3√7 / 7
Q5. Rationalise: 2/(3√2)
A: = 2√2 / (3×2) = √2/3
Exercise 3.3 – Rationalising Using Conjugates
Q1. Rationalise: 1 / (√5 + 2)
A: Multiply by conjugate (√5 – 2)
⇒ (√5 – 2) / [(√5 + 2)(√5 – 2)] = (√5 – 2)/(5 – 4) = (√5 – 2)/1 = √5 – 2
Q2. Rationalise: 1 / (3 – √2)
A: = (3 + √2) / [(3 – √2)(3 + √2)] = (3 + √2)/(9 – 2) = (3 + √2)/7
Q3. Rationalise: 1 / (√3 + √2)
A: Multiply by (√3 – √2)
⇒ (√3 – √2) / [(√3 + √2)(√3 – √2)] = (√3 – √2)/(3 – 2) = √3 – √2
Q4. Rationalise: 2 / (√6 – 1)
A: = 2(√6 + 1) / (6 – 1) = 2(√6 + 1)/5
Q5. Rationalise: 5 / (2 + √3)
A: = 5(2 – √3)/(4 – 3) = (10 – 5√3)/1 = 10 – 5√3
Exercise 3.4 – Simplifying Complex Rational Expressions
Q1. Simplify: (√3 – √2)(√3 + √2)
A: = 3 – 2 = 1
Q2. Simplify: (√5 + 1)²
A: = (√5)² + 2√5 + 1 = 5 + 2√5 + 1 = 6 + 2√5
Q3. Simplify: (√2 + √3)²
A: = 2 + 2√6 + 3 = 5 + 2√6
Q4. Simplify: (√7 – √5)(√7 + √5)
A: = 7 – 5 = 2
Q5. Simplify: (√a + √b)(√a – √b)
A: = a – b
Why RD Sharma Class 9 Chapter 2 Maths is Important
Builds Strong Foundation in Algebra: It helps you understand how to deal with irrational numbers and simplify expressions, which is essential for higher-level algebra.
Boosts Calculation Speed: Rationalising the denominator makes expressions easier to handle in exams, improving speed and accuracy.
Useful in Real Life & Higher Classes: Rational numbers and surds appear in Class 10, 11, 12 Maths, Physics, and even in competitive exams like JEE/NEET.
Scoring Chapter in Exams: The steps are simple and formula-based, so with practice, you can score full marks.
Helps in Understanding Number System Deeply: It improves your grasp on how numbers work, including square roots and surds, making you more confident in maths overall.
RD Sharma Solutions for Class 9 Maths Chapter 3 Rationalisation
In Chapter 3 of RD Sharma Class 9 Maths – Rationalisation, students learn key concepts like:
- Introduction to Rationalisation
- Rationalising the Denominator
- Important Algebraic Identities
By practising these exercises, students will understand different ways to solve problems easily and gain confidence for exams. That’s why it’s strongly recommended to go through all the solutions in this chapter to score better in the final exams.
FAQs on RD Sharma Solutions Class 9 Maths Rationalisation
How many exercises are present in RD Sharma Solutions for Class 9 Maths Chapter 3?
There are 4 exercises in Chapter 3 – Rationalisation. Each exercise focuses on a different type of question, including simplifying surds, rationalising the denominator, using conjugates, and applying algebraic identities.
Why should I opt for RD Sharma Solutions for Class 9 Maths Chapter 3?
RD Sharma Solutions provide step-by-step explanations that make concepts easy to understand. They help you practise different types of questions, clear doubts, and boost your confidence for school exams and competitive tests.
Is RD Sharma Solutions for Class 9 Maths Chapter 3 difficult to learn?
Not at all! With regular practice and proper guidance, this chapter is easy and scoring. RD Sharma breaks it down into simple steps, so you can understand and solve problems without confusion.
What is rationalisation in mathematics?
Rationalisation is the process of removing surds (square roots) from the denominator of a fraction. It helps make the expression simpler and easier to use in calculations.
How can I rationalise the denominator?
You can rationalise the denominator by multiplying the numerator and denominator with a suitable value, like the same surd or its conjugate, depending on the expression. For example, to rationalise 1/√2, multiply by √2/√2 to get √2/2.
Why is it important to understand rationalisation?
Rationalisation improves your ability to simplify expressions and is a skill required in many advanced topics in algebra, geometry, and trigonometry. It also improves calculation speed and accuracy in exams.
How can RD Sharma Class 9 Solutions for Chapter 3 help me?
The solutions provide detailed explanations, shortcuts, and multiple solving methods. Practising them helps you master rationalisation techniques and prepares you well for your school exams.