Question

Prove that square root of 3 is irrational.

Answer 1

let √3 be a rational number 
i.e. √3 = a/b where a,b ∈ integers having no common factor other then 1 and b≠0
= √3 = a/b
 square both the sides
= 3= a²/b2
= a² = 3b²
= b² = a²/3
= 3 divides a²
= 3 divides a²
 let a²= 3c
= b²=9c²/3
= b²= 3c²
= c²= b²/3
= 3 divides b²
= 3 divides b
thus 3 is a common factor of a and b
this contradicts the fact that a and b are coprime numbers i.e. having no common factor other then 1.
therefore √3 is not a rational number 
hence it is irrational
hope it helps u.please mark it as the best.

Answer 2

Answer:

Let √3 be a rational number  

i.e. √3 = a/b where a,b ∈ integers having no common factor other then 1 and b≠0

= √3 = a/b

square both the sides

= 3= a²/b2

= a² = 3b²

= b² = a²/3

= 3 divides a²

= 3 divides a²

let a²= 3c

= b²=9c²/3

= b²= 3c²

= c²= b²/3

= 3 divides b²

= 3 divides b

thus 3 is a common factor of a and b

this contradicts the fact that a and b are coprime numbers i.e. having no common factor other then 1.

therefore √3 is not a rational number  

hence it is irrational

hope it helps u.please mark it as the best.

Step-by-step explanation: