Instant Squares for Numbers Ending in 5!

Ever wondered if there's a super-fast way to square numbers like 35, 75, or even 105 without a calculator? There is, and it's shockingly simple!

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

The Trick

To square any number ending in 5 (e.g., $N5$): 1. Ignore the '5' and take the digit(s) before it, let's call this $N$. 2. Multiply $N$ by the next consecutive integer, $(N+1)$. 3. Append '25' to the result from step 2. That's it! **Why it works:** Any number ending in 5 can be written as $(10N+5)$. Squaring this gives $(10N+5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. This shows we calculate $N(N+1)$ and then effectively multiply by 100 and add 25, which is achieved by appending '25'.

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