| It is amazing anyone could have the slightest problem understanding
| Dirk's point.  Apparently in the world you and Androcles inhabit
| there is no ambiguous way to write the positive number x such that
| x*x=2.
|
| The equation x^2=N has two roots.  Those two roots are sqrt(N) and -sqrt(N).
| Apparently you and Androcles think the two roots are sqrt(N) and sqrt(N)
| and have no way of distinguishing the two roots from each other,

That is quite correct. There is no way to distinguish the two roots from
each other, just as there is no way to determine the sign of x from the
symbol alone. If you can tell me the sign of x, do so, but please do not
insist sqrt(N) is positive.

| or of specifying which root you mean.

That is NOT correct, I CAN specify which root I mean.
Androcles