The '5' Squaring Secret!

Ever stare at $45^2$ and wish for a magic button? What if I told you there's a super-fast way to square *any* number ending in 5, all in your head?

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

The Trick

Here's the trick: Take the digit(s) *before* the 5. Let's call this 'n'. Multiply 'n' by ($n+1$). Then, simply append '25' to the result. That's it! \n\nWHY it works: Any number ending in 5 can be written as $(10n + 5)$. Squaring this gives $(10n + 5)^2 = (10n)^2 + 2(10n)(5) + 5^2 = 100n^2 + 100n + 25 = 100n(n+1) + 25$. The $n(n+1)$ part forms the leading digits, and multiplying by 100 shifts it, effectively appending 25.

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