At a parade rehearsal, 2000 soldiers are to form the largest possible solid square block with equal rows and columns. Those who do not fit stand aside. How many soldiers stand aside?

Useful patterns to spot a perfect square (and reject non-squares):

- **Last digit**: a perfect square ends in 0, 1, 4, 5, 6, or 9 — NEVER in 2, 3, 7, or 8. So 142 cannot be a perfect square (ends in 2).
- **Number of zeros at the end**: must be even. 100 is a perfect square $(10^2)$; 1000 is not.
- **Squares of even numbers are even; squares of odd numbers are odd.**
- **Sum of consecutive odd numbers**: 1 + 3 + 5 + … + $(2n-1)=n^2$. Try it: $1+3+5=9=3^2$.

These let you reject many candidates without doing any heavy work.