Squaring Numbers Ending in 5 - Lightning Fast!

Ever wished you could square numbers ending in 5 in seconds, without a calculator? Prepare to impress your friends and ace your tests!

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

The Trick

To square any number ending in 5, ignore the 5 for a moment. Take the digit(s) *before* the 5, let's call this 'x'. Multiply 'x' by $(x+1)$. Finally, just append '25' to the end of your result. That's it! \n\nWHY it works: If a number is $10x+5$, its square is $(10x+5)^2 = 100x^2 + 100x + 25 = 100x(x+1) + 25$. The $100x(x+1)$ part represents placing 'x(x+1)' in the hundreds and thousands place, and $+25$ adds the trailing '25'.

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