Squaring Secrets for Numbers Ending in 5!

Ever wished you could square big numbers ending in 5 in seconds, without a calculator? Prepare to impress!

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

The Trick

Got a number ending in 5, like $N5$? Here's the magic: Take the digit(s) before the 5 (let's call it $N$). Multiply $N$ by the next consecutive integer, $(N+1)$. Finally, simply append '25' to the end of your result! That's it! Why it works: A number like $N5$ can be written as $(10N+5)$. Squaring this gives $(10N+5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100N(N+1) + 25$. So, we compute $N(N+1)$ and then effectively multiply by 100 (adding two zeros) and add 25 (replacing the zeros with 25).

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