Squaring Numbers Ending in 5!

Ever struggled to quickly square numbers like 35 or 75 without a calculator? There's a super-fast secret that makes it trivial!

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

The Trick

To square any number ending in 5, follow two simple steps: \n1. Take the digit (or digits) before the 5. Let's call this 'n'. \n2. Multiply 'n' by $(n+1)$. \n3. Append '25' to the result of step 2. That's your answer! \n\nWHY it works: This trick comes from the algebraic expansion $(10n+5)^2 = (10n)^2 + 2(10n)(5) + 5^2 = 100n^2 + 100n + 25 = 100n(n+1) + 25$. The $n(n+1)$ part forms the initial digits, and the $+25$ is simply appended.

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