Mathematics

You're looking for two consecutive perfect squares—like $n^2$ and $(n+1)^2$—whose difference is exactly 63. The key insight is that the difference between consecutive perfect squares follows a simple pattern: $(n+1)^2 - n^2$ always expands to a linear expression in $n$. Set that equal to 63 and solve for $n$, then verify your answer.

You're looking for two consecutive perfect squares—like $n^2$ and $(n+1)^2$—whose difference is exactly 63. The key insight is that the difference between consecutive perfect squares follows a simple pattern: $(n+1)^2 - n^2$ always expands to a linear expression in $n$. Set that equal to 63 and solve for $n$, then verify your answer.