Question

Is 2/root3 a rational or irrational number.

Answer 1

Let us assume that 1/2+root 3 is rational .
So 1/2+root 3 = a/b where a and b are irrationals.
Now arranging the equation we get 1=a/b * 2+root 3
so root 3 = 1-a/b -2
since rhs is a rational number root 3 should be also rational .
But this contradicts the reality that root 3 is irrational .
So our assumption is wrong and hence we conclude that is irrational.