I've been thinking about this recently and couldn't find the answer to my question (even though I assume it's a really simple one, so forgive me if it's too trivial). Let's say we have two rods of length 1 meter and we put them at right angles to each other. Then we cut a third rod just long enough to connect the non-touching ends of the first two rods - now we have a right isosceles triangle. Question: what's the length of the hypotenuse? Clearly the answer is √2 Now suppose we physically measured the length of the rod which is the hypotenuse (maybe by multiplying the number of atoms on top of each other times the length of each atom?) Aren't we going to get a rational number as a result?