Question

how can we proof that 3+√3 is irrational .explain​

Answer 1

Let us assume 3-√3 is rational

let 3-√3 = a/b (a,b are any integers)

=> 3 - a/b = √3

=> √3 = 3 - a/b

=> √3 = 3b-a/b

For any two integers, RHS (3b-a/b) is rational

But, LHS(√3) is irrational

A rational and irrational are never equal

So, our assumption is false

Therefore, 3-√3 is irrational