# Prove that 3+2√3 is irrational .

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Solution :

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

So, x= 3+2√3

x2=(3+2√3)

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 .