Let us assume that 1/√3 is rational
1/√3 x √3/ √3 = √3/3 is rational
Which is only possible if 1/3 is rational and √3 is rational. As we know that, Product of two rational numbers is rational
But the fact is, √3 is an irrational.
Which is contradictory to our assumption.
which implies 1/√3 is irrational. Hence proved.