Socrates: Let's try odd over even next, shall we?
Boy: Fine.
Socrates: What happens when you multiply an even number by an even number, what kind of number do you get, even or odd?
Boy: Even, of course. An even multiple of any whole number gives another even number.
Socrates: Wonderful, you have answered two questions, but we need only one at the moment. We shall save the other. So, with odd over even, if we multiply any of these times themselves, we well get odd times odd over even times even, and therefore odd over even, since odd times odd is odd and even of even is even.
Boy: Yes. A ratio of odd over even, when multiplied times itself, yields odd over even.
Socrates: And can our square root of two be in that group?
Boy: I don't know, Socrates. Have I failed?
Socrates: Oh, you know, you just don't know that you know.
Try this: after we multiply our number times itself, which the learned call "squaring" the number which is the root, we need to get a ratio in which the first or top number is twice as large as the second or bottom number. Is this much correct?