I was wondering, given a square that is $1 \times 1$, how can we know that the diagonal is an irrational length geometrically??? We could use the Pythagorean Theorem to see that the diagonal of a square is $\sqrt{2}$... But how can a finite length have an infinite sequence of numbers.... I think there's two main questions then :
How to determine geometrically that a length is irrational and How can a finite length be irrational ?
Thank you!