Boy: I should hope and pray not.
Socrates: Well today, you are going to tell us some things about that number, which when multiplied by itself gives us two.
Boy: I will tell you everything I know, or think I know,
Socrates, and hope that I am correct or can be corrected.
Socrates: To Meno, surely he is a fine boy, eh Meno?
Meno: Yes, I am proud to own him, but I don't see how he can be smart enough to do the work today that would take a Pythagorean monk ten years of cloistered life to accomplish.
Socrates: We shall see. Boy, you are doing fine. I think I could even make a scholar of you, though I fear you might turn to wine and women with your new found wealth, if you succeed, rather than continue to polish the wit which should get you that reward.
Boy: I don't think I would want to spend that much time with women or with wine, Socrates.
Socrates: You will find something, no doubt. So, back to the number which when square gives us two. What can we say about such a number? Is it odd or even? Well it would have to be a whole number to be one of those, would it not, and we saw the other day what happens to whole numbers when they are squared? They give us 1,4,9 and 16 as square areas, did they not?
Boy: Yes, Socrates, though I remember thinking that there should have been a number which would give eight, Socrates?
Socrates: I think we shall find one, if we keep searching. Now, this number, do you remember if it had to be larger or smaller than one?