The 'Ends in 5' Squaring Secret!

Ever wish you could square big numbers like $35^2$ or $75^2$ in seconds, all in your head? Get ready to amaze yourself and your friends with this simple math magic!

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

The Trick

To square any number ending in 5, follow these two super easy steps: 1. The answer will always end in '25'. 2. Take the digit(s) before the '5'. Let's call this number 'n'. Multiply 'n' by the next consecutive integer (n+1). 3. Place the result from step 2 in front of '25'. That's your answer! **Why it works:** Any number ending in 5 can be written as $(10n + 5)$. Squaring this gives $(10n + 5)^2 = 100n^2 + 100n + 25 = 100n(n+1) + 25$. This clearly shows that the result is $n(n+1)$ followed by $25$.

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