Squaring Numbers Ending in 5!

Ever need to quickly square a number like 35, 75, or even 125 without a calculator? What if I told you there's a super-fast way to do it in your head?

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

The Trick

To square any number ending in 5 (e.g., $D5$), simply follow two steps: 1. Take the digit(s) before the 5 (let's call it $D$). 2. Multiply $D$ by $(D+1)$. 3. Write '25' after the result from step 2. Why it works: A number ending in 5 can be written as $(10D + 5)$. Squaring this gives $(10D + 5)^2 = (10D)^2 + 2(10D)(5) + 5^2 = 100D^2 + 100D + 25 = 100D(D+1) + 25$. This shows the first part is $D(D+1)$ times 100 (meaning it forms the leading digits), followed by $25$.

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