It can be done trivially with 48 squares, just connect $(i,i)$ to $\left(25\left[\frac{25-i}{25}\right],25\left[\frac{25-i}{25}\right]\right)$ and $(i,-i)$ to $\left(25\left[\frac{25-i}{25}\right],-25\left[\frac{25-i}{25}\right]\right)$, where $[...]$ denotes round(...). Now can it be done with 47? No, consider the 24 inner horizontal lines and 24 inner vertical lines. None of them can be covered by just 1 square, so we need at least 2 squares per line, and since a square has 4 sides we need at the very least $\frac{2.24.2}{2}=48$ lines.