Squaring Numbers Ending in 5 Fast!

Ever need to quickly square a number like 35 or 75? Stop multiplying the long way! There's a lightning-fast secret!

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

The Trick

Want to square a number ending in 5, like $N5$? Here's how: 1. The last two digits of your answer will ALWAYS be $25$. 2. Take the digit(s) before the $5$ (let's call it $N$). 3. Multiply $N$ by the next consecutive integer, $(N+1)$. 4. Combine the result from step 3 with $25$. WHY it works: This trick comes from expanding $(10N + 5)^2$. This equals $(10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. The $100$ factor places $N(N+1)$ in the hundreds place, followed by $25$.

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