Squaring Numbers Ending in 5!

Ever wondered how some people can square large numbers like 35 or 105 in seconds, without a calculator? There's a super-fast secret!

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

The Trick

To square any number ending in 5, follow these two simple steps: 1. Ignore the '5' for a moment. Take the digit(s) before the 5. Let this number be $x$. 2. Multiply $x$ by $(x+1)$. This product forms the first part of your answer. 3. Finally, just append '25' to the end of your result from step 2. **WHY it works:** A number ending in 5 can be written as $10x+5$. Squaring it gives $(10x+5)^2 = (10x)^2 + 2(10x)(5) + 5^2 = 100x^2 + 100x + 25 = 100x(x+1) + 25$. This shows $x(x+1)$ is multiplied by 100, meaning '25' is simply appended.

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