Sorry for my late post, George.

For the other thing:

There' s more generalized formula:

Let Q be the set of all retional numbers:

Q={p/q|p,q ∈ N}, where N = {1,2,3...}

Let Ir is the set of all numbers of the kind x^(1/y):

Ir={x^(1/y)|x,y ∈ N}.

Then:

Q || Ir = N.

Proof:

Let a,b,c,d ∈ N and

But d ∈ N => exists k ∈ N : k^c=d.

But then

.

Particularry, this means that if an integer n is not a square, then √n is irrational.