Square It Quick: Numbers Ending in 5

Ever need to quickly square a number like 25 or 75? There's a super-fast trick that makes it a breeze, no calculator needed! Intrigued?

Subject: mental-calculation • Classes: 6–12 • Difficulty: basic

The Trick

To square any number ending in 5 (e.g., $N = 10n + 5$): 1. Identify the digit(s) before the 5. Let this be $n$. 2. Multiply $n$ by the next consecutive integer, $(n+1)$. 3. Append '25' to the result of step 2. Why it works: $(10n+5)^2 = (10n)^2 + 2(10n)(5) + 5^2 = 100n^2 + 100n + 25 = 100n(n+1) + 25$. This means the first part is $n(n+1)$ multiplied by 100, effectively adding '25' at the end.

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