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# NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No.1 Solutions : Prove that √5 is irrational

Hy Friends Welcome On NCERT MATHS SOLUTIONS !! Today we are going to solve the Question : ”Prove that √5 is irrationalof Exercise 1.3 Question No 1 Solutions (Real Numbers) of Class 10th, which will prove to be very helpful for you.

# CBSE/NCERT MATHS Class 10 Ex- 1.3 Q No.1 Solutions

If you are a student of CBSE, today we are going to give you the CBSE / NCERT Chapter : Real Numbers Exercise 1.3 Question No – 1 Solutions . Hope you like this post about Class 10th Maths Solution.

Here we would like to tell you that there are other websites on which the students demanded the Solution of NCERT MATHS Chapters, we had promised them that we will soon send you the questions of Class 9, And we completed our promise to them.We asked the good knowledgeable teachers of mathematics and asked them to solve the issues of CBSE’s mathematical questions and also said that the answers to our questions are such that the students have no difficulty in solving all those questions.

### Real Numbers CHAPTER : 1

Symbol of real numbers (ℝ) In mathematics, the real number is the value presented to any amount corresponding to the simple line. Actual numbers include all rational numbers such as -5 and fractional numbers such as 4/3 and all irrational numbers such as √2 (1.41421356 …, square root of 2, an unregulated algebraic number). By incorporating the ample numbers in the actual numbers, they can be presented from the eternal points that can be attributed on a line in the form of a real number line.

### Class 10 Exercise 1.3 Question No. 1 Solutions

Let √5 is a rational number.

Therefore, we can find two integers a, b (b≠0) such = √5 = a/b Let a and b have a common factor other than 1. Then we can divide them by the common factor, and assume that a and b are co- prime.

a =  b

a2 = 5b2

Therefore, a2 is divisible by 5 and it can be said that a is divisible by 5.

Let a = 5k, where k is an integer

(5k)2 = 5b2

5k2 = b2

This means that b2 is divisible by 5 and hence, b is divisible by 5. This implies that a and b have 5 as a common factor. And this is a contradiction to the fact that a and b are co-prime. Hence, √5 cannot be expresswed as p/q or it can be said that √5 is irrational .