Quick Square: Numbers Ending in 5!

Ever need to quickly square a number like 35 or 75? Stop using calculators! There's a lightning-fast trick!

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

The Trick

To square any number ending in 5, say $N5$, just ignore the 5 for a moment. Take the digit(s) before the 5, let's call it $X$. Multiply $X$ by $(X+1)$. Then, simply append '25' to the result. That's it! Why it works: $(10X+5)^2 = (10X)^2 + 2(10X)(5) + 5^2 = 100X^2 + 100X + 25 = 100X(X+1) + 25$. This means the product $X(X+1)$ determines the hundreds and higher places, and 25 is always at the end.

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