Question

prove that square root of 2 + square root of 3 are irrational

Answer 1

Hi Renuka,

Lets think root of 2 + root of 3 = x
Then, 2 + 2 root 6 + 3 = x square
Root 6 = x square - 5
As the set of rational numbers is closed under multiplication and addition x square - 5 is irrational and we even know that root 6 is irrational.

So root 2 + root 3 is irrational

Answer 2

Answer:

Explanation: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.