Squaring Numbers Ending in 5 - Fast!

Want to impress your friends with lightning-fast calculations? Learn this trick to square any number ending in 5 in seconds!

Subject: mental-calculation • Classes: 6–12 • Difficulty: basic (6-8)

The Trick

To square a number ending in 5, like 35, first take the digit(s) before the 5 (in this case, 3). Multiply that digit by the next higher digit (3 * 4 = 12). Then, simply append 25 to the end of the result. So, $35^2 = 1225$. Why does it work? A number ending in 5 can be written as $10n + 5$. Squaring it, we get $(10n + 5)^2 = 100n^2 + 100n + 25 = 100n(n+1) + 25$. The trick essentially calculates $n(n+1)$ and then multiplies it by 100 and adds 25.

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