Question

In a square with integer side lengths, is it possible to find a point that's a rational number length away from all 4 corners?

Answer 1

I believe that it's not possible.

Answer 2

Give an example, because this is an unproven problem in number theory. :)

Answer 3

\[h=\frac{1}{\sqrt{2}}a \cancel{ \in} \mathbb{Q}\]