Find the smallest integer that must be added to $2037$ so that the resulting number is a perfect square. State the integer and the perfect square.

Step-by-step solution

1. Estimate $\sqrt{2037}approx45.15$.
2. The next integer after $45$ is $46$, and $46^2=2116$.
3. Check that $2116>2037$ and is a perfect square.
4. Compute the difference: $2116-2037=79$.
5. Thus add $79$ to get $2116=46^2$.
6. So the integer to add is $79$ and the perfect square obtained is $2116$.

Concept tested: Nearest perfect square

Published 4 October 2026 · How this solution was prepared and checked