Originally Posted by

**farmeruser1** Pardon my naivety, but I have never worked with Integer square roots before, Let me give this a crack.

To answer your first question, if √n is rational, then √n=q/p, which is p√n=q, q is a positive integer, as wanted.

Now, the next one, if we expand we get k√n-k[√n]. k√n is an integer that we just proved above, and k[√n] is a positive smaller integer by definition.

So we have (√n-[√n])k is a positive integer.

The next part by definition, <0(√n-[√n])<1 so this multiplied by some k is <k.

Now the last part, lets expand, kn-k√n[√n], which by using the last 2 parts we know is a positive integer.

Now because k√n<k, then it cannot be rational, is this correct?