What is the smallest integer that must be added to $245$ so that the resulting number is a perfect square?

Step-by-step solution

1. Find the integer part of $\sqrt{245}$: $\sqrt{245}\approx 15.65$, so the next integer is $16$.
2. Calculate the next perfect square: $16^2=256$.
3. Determine the difference between this square and $245$: $256-245=11$.
4. Thus adding $11$ to $245$ yields $256$, which is a perfect square.

Concept tested: Nearest perfect square

Published 22 August 2026 · How this solution was prepared and checked

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