What is the argument that Greeks used to prove that square root of 2 cannot be expressed as a fraction?

Answer 1

the greeks used a demonstration close to that one http://www.math.utah.edu/~pa/math/q1.html

It's a simple proof by contradiction.


Not having read the original document (in greek), I can't say it for sure, but from what I found on the net, they used that demonstration. (at least, that idea)

Answer 2

Actually the proof goes something like this,

assume it is rational root(2) = p/q

2p^2 = q^2..... so that p and q should have common factor (2) but this is not possible since we assumed p/q doesn't have common factors....(see previous link)

Actually using this argument we could prove that any nonsquare number's square root is irrational.

Answer 3

Because it is ir-rational number