prove that 1/?2 is irrational.

Answer :

Let us assume that 1/2^1/2 is rational.

Then it is of the form p/ q where pand q are co prime integers and q is not equal to zero

It implies  1/2^1/2 = p/ q

It implies q/ p =  2^1/2

It implies that 2^1/2 is rational

But this contradicts to the fact that  2^1/2 is irrational. So our supposition is wrong.

Hence  1/2^1/2  is rational