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NCERT Solutions for Class 10 Maths Chapter 1 Ex 1.3 

 

NCERT Solutions for Class 10 Maths Chapter 1 Ex 1.3 are based on irrational numbers. In this exercise, you have to find whether a number is irrational or not. There are just three questions in the exercises and all are important from the exam perspective. Practising these questions will make it easier for you to tackle such questions in the board exam or even in competitive tests. The askIITians Maths experts have provided stepwise solutions for this exercise to help you understand the concepts of irrational numbers in a better way. Let us see what is included in this exercise and how you can download the NCERT Solutions for free. 

About NCERT Class 10 Maths Chapter 1 Real Numbers Ex 1.3 

In Class 9, you have already studied what are rational and irrational numbers. You have also studied how to locate irrational numbers on a number line. In Class 10, you will study √p is irrational, given that p is a prime number. Here are a few points to remember before you start solving this exercise:

  • A number ’s’ is called irrational number if it cannot be written in the form, pq where p and q are integers and q ≠ 0. 
  • Let p be a prime number. If p divides a2 , then p divides a, where a is a positive integer. 
  • According to the Fundamental Theorem of Arithmetic, every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. 
  • The sum or difference of a rational and an irrational number is irrational. 
  • The product and quotient of a non-zero rational and irrational number is irrational.

Types of questions included in NCERT Class 10 Maths Chapter 1 Real Numbers Ex 1.3:

 

In this exercise, you are given three questions and in all of them, you are given some numbers. You have to prove that they are irrational. For instance, in question 1, you have to prove that √5 is irrational. In question 2, you have to prove that 3 + 2√5 is irrational. You must know the steps on how to solve these questions so that you can solve any type of such questions in the board exams. 

Download Free NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 

 

Revise all the questions of Class 10 Maths Chapter 1 Ex 1.3 with our NCERT Solutions. We have also included NCERT Solutions for all other exercises of the chapter so that you can prepare well for your board exam. The main topics of this chapter include Euclid’s Division Lemma, Rational and Irrational Numbers, and the Fundamental Theorem of Arithmetic. Questions in this chapter are based on finding the HCF and LCM of given integers, proving that the given numbers are irrational, and identifying whether the given numbers ​​have a terminating decimal expansion or a non-terminating repeating decimal expansion without actually dividing the numbers. 

 

Download exercise-wise solutions for the Real Numbers chapter for free from the links given below:

  • NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.1 
  • NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.2 
  • NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 
  • NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.4

NCERT Class 10 Maths Chapter 1 Ex 1.3 FAQs

 

1. How to download the NCERT Solutions for Ex 1.3 of Chapter 1 Real Numbers? 

We have provided stepwise solutions for NCERT Class 10 Maths Chapter 1 Ex 1.3 in PDF form. You can download them for free from the link given on this page. We have also provided separate solutions for all other exercises of this chapter. 

 

2. How many questions are there in Ex 1.3 of Chapter 1 Real Numbers? 

There are 3 questions in Ex 1.3 of Chapter 1 Real Numbers. Exercise 1.1 includes 5 questions. Exercise 1.2 includes 7 questions. Exercise 1.3 includes 3 questions. 

 

3. What is the fundamental theorem of arithmetic? 

According to the Fundamental Theorem of Arithmetic, every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.


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