Question

OLA
19. Prove that 3 + V3 is irrational.​

Answer 1

$answer$

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 wrong

Therefore, 3+√3 is irrational

Answer 2

Answer:

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 wrong

Therefore, 3+√3 is irrational