Question

Prove that 3+2√3 is irrational .

Answer 1

Let us assume that  3+2√3 is rational .

So, x= 3+2√3

x²=(3+2√3)² 

x²=21+12√3

√3=(x²−21)/12…….(1)

 because x is a  rational number

So, the expression  (x²−21)/12 is also a rational number.This is a contradiction .Hence, 3+2√3 is irrational .