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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.

TextbookNCERT
BoardCBSE
CategoryNCERT Solutions
ClassClass 10
SubjectMaths
ChapterChapter 1
ExerciseClass 10 Maths Chapter 1 Real Numbers Exercise 1.3
Number of Questions Solved3
NCERT Solutions For Class 10 Maths Chapter 1 Real Numbers Ex 1.3

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

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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