NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers Ex 1.3
Here, Below you all know about NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3 Question Answer. I know many of you confuse about finding these Chapter 1 Real Numbers Ex 1.3 Of Class 10 NCERT Solutions. So, Read the full post below and get your solutions.
Textbook | NCERT |
Board | CBSE |
Category | NCERT Solutions |
Class | Class 10 |
Subject | Maths |
Chapter | Chapter 1 |
Exercise | Class 10 Maths Chapter 1 Real Numbers Exercise 1.3 |
Number of Questions Solved | 3 |

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.3
NCERT TEXTBOOK EXERCISES
Question 1. Prove that √5 is irrational.
Solutions:
Let us assume that is rational.
∴ There exists co-prime integers a and b (b ≠ 0) such that
√5 = a/b ⇒ √5b= 0
Squaring on both sides, we get
5b2= a2…… (i)
⇒ 5 divides a2 ⇒ 5 divides a
So, we can write a = 5c for some integer c.
From (i) and (ii)
5b2 = 25c2
⇒ b2 = 5c2
⇒ 5 divides b2
⇒ 5 divides b
∴ 5 is a common factor of a and b.
But this contradicts the fact that a and b are co-primes.
This contradiction has arisen because of our incorrect assumption that √5 is rational.
Hence, √5 is irrational.
Question 2. Prove that 3 + 2√5 is irrational.
Solutions:
Let us assume that 3 + 2√5 is rational.
∴ There exists co-prime integers a and b(b ≠ 0) such that

But this contradicts the fact that √5 is irrational.
This contradiction has arisen because of our incorrect assumption that 3 + 2√5 is rational. Hence, we conclude that 3 + 2√5 is irrational.
Question 3. Prove that the following are irrational.

Solutions:


NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.3 PDF
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