**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 irrational****” **of** 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.

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**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.

**Exercise- 1.3 Question No. 1 : Prove that √5 is irrational**

**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**

** a ^{2} = 5b^{2}**

Therefore, a^{2} 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} = 5b^{2}**

**5k ^{2} = b^{2}**

This means that b^{2} 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 .

**CLICK ON RED BOX FOR CBSE Maths Class 10 Exercise 1.3 Real Numbers Next Question Answer :-**

**NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No.2 Solutions : Prove that √5 is irrational**

**SEE NCERT Maths Class 10 Chapter 1 Ex-1.3 All Questions Solutions **

**NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No.1 Solutions : Prove that √5 is irrational****NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No. 2 Solutions : Prove that 3 + 2 √5 is irrational.****NCERT/CBSE MATHS Class 10 Ex- 1.3 Q No. 3 Solutions : Question 3 : Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2**

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