# NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.3 Real Numbers

NCERT solutions for class 10 maths chapter 1 exercise 1.3 Real Numbers enables the students to revisit the concept of irrational numbers. There is a very important theorem that falls in this section which is stated as “let p be a prime number. If p divides a^{2}, then p divides a, where a is a positive integer”. This exercise is mainly based on the concept of proving if a number is irrational. To solve such a problem we assume that the given number is rational. By integrating the theorem mentioned above we use contradicting proof and verify that the given number is indeed irrational. NCERT solutions class 10 maths chapter 1 exercise 1.3 consists of 3 questions, out of which 2 problems are easy while 1 is in the long answer type format.

Another critical point to note while exploring this exercise is that the sum of a rational and an irrational number is irrational. Additionally, the product and quotient of a non-zero rational and irrational number are irrational. These are statements that will also help in proving that a number is irrational. Class 10 maths NCERT Solutions chapter 1 exercise 1.3 Real Numbers are available in a scrollable PDF format, the link of which is provided below.

**ā** Download NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.3

**Exercise 1.3 Class 10 Chapter 1 **

### More Exercises in Class 10 Maths Chapter 1

- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.1
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.2
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.4

## NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.3 Tips

NCERT solutions class 10 maths chapter 1 exercise 1.3 Real Numbers covers questions based on proving whether a number is irrational or not. In order to do so, students can use a simple technique of assuming it is a rational number and then try to express the number in the form of p/q, where p and q are integers. If this is not possible, students can proceed to the next step.

NCERT solutions for class 10 maths chapter 1 exercise 1.3 explains the method of contradiction in real numbers which is based on the technique of assuming that a given statement is true. So, while proving the statement, if we arrive at results that contradict our assumption, we prove the contrary. For example, if we have to prove √5 is irrational, we will assume it is rational.

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