RD Sharma Class 9 Chapter 3 Solutions (Rationalisation)

RD Sharma Class 9 Maths Solutions for Chapter 3 are prepared to aid you in solving the exercise questions of Rationalisation with absolute clarity in the concepts. In this chapter of RD Sharma Solutions, you will learn about the application of previously learnt algebraic identities and some new identities. You will also get to know the step by step procedure of rationalising the denominators of the given numbers. This chapter will help you develop a good understanding of real numbers and the operations related to them. This is a scoring chapter and with adequate practice, you can ensure full marks in this chapter easily.

There are 8 questions in the 2 exercises of this chapter and another VSAQ exercise consisting of 9 questions. The questions in the RD Sharma Class 9 Maths Chapter 3 range from beginner level questions to advanced level questions. Practising these questions thoroughly will help you score high in the school exams as well as other national level competitive exams. These exercises are also crucial for building a strong aptitude which will help you in higher studies. Besides, all the advantages you can think of, the most important is that you will learn to manage your time well in the high-pressure environment of the exam hall.

Our solutions are prepared with the intent to provide you with a one-stop solution for your academic needs in maths. The expert team at Instasolv has researched extensively to list all the recurring doubts of students and have addressed them all in the RD Sharma Class 9 Maths Solutions for Chapter 3. Therefore, if you stumble upon a query while studying, just reach out to the Instasolv platform for on-point guidance to make efficient use of your study hours. These solutions are updated timely so you can use them directly in your exams.

Important Topics for RD Sharma Solutions for Class 9 Chapter 3: Rationalisation


There are some numbers that remain complicated to perform operations of them such as surds. The numbers that are left in the root form are termed as surds. Surds are irrational numbers. You can rationalise the denominator of a surd, sayby multiplying the numerator and denominator by the same surd, such multiplying, in this case, will give you the rationalised form as.

Conjugate of Surds

The first step to rationalise the denominator of a number is to find its conjugate. A conjugate of a surd is when we change the sign between two simple surds. For instance, the conjugate of a number of the typewill be. Conjugates are used to multiply with the radical denominator of the number which is to be rationalised. It is vital to memorise all the identities learnt so far as to be able to understand the procedure of rationalisation.

Steps to Rationalise a Surd

To rationalise a given number in the exercise questions, you should follow the steps given below:

  1. Firstly, find the conjugate of the denominator.
  2. Multiply the numerator and the denominator of the number with this conjugate.
  3. Check if any of the identities such as a2b22 apply to the condition so formed in the denominator.
  4. Simplify the solution.

Exercise Discussion for RD Sharma Solutions for Class 9 Chapter 3: Rationalisation

  1. There are a total of 17 questions in the RD Sharma Class 9 Maths Solutions for Chapter 3 including the VSAQ exercise. The questions are based mainly on the identities that you studied in the previous chapters.
  2. There are 4 questions in exercise 3.1. You will be required to simplify the mathematical ratios and rational equations using the properties of rational numbers in these questions.
  3. The 4 questions in exercise 3.2 have various sub-sections in which you will have to rationalise the given numbers to make your calculations easier. 
  4. You will be required to use all the identities learnt in the number systems explicitly to achieve your desired results.
  5. There is an additional exercise consisting of VSAQs. The questions are 9 in number covering topics such as laws of exponents in real numbers and rationalisation of the given complicated set of numbers using identities.

Benefits of RD Sharma Solutions for Class 9 Chapter 3: Rationalisation by Instasolv

  1. The maths experts of Instasolv will provide you with tips and tricks to solve the rationalisation problems easily.
  2. The  RD Sharma Solutions for Class 9 Chapter 3 ‘Rationalisation’ at the Instasolv platform are completely free of cost and easy to access. 
  3. Instasolv solutions are both inclusive and interactive in nature at they cover each and every question with adequate reasoning at every step. 
  4. You will get to convert your efforts in studying into marks if you refer to Instasolv to clear your queries.
  5. Instasolv experts have written all the answers on this platform in compliance with the latest CBSE guidelines for Class 9.
  6. The set of solutions at Instasolv are written in an easy and understandable language.