Instant Squares for Numbers Ending in 5!

Ever wished you could square numbers like 35 or 75 in your head almost instantly? There's a super cool trick that makes it feel like magic!

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

The Trick

To square any number ending in 5, say $N5$: \n1. Take the digit(s) before the 5 (let's call it $D$).\n2. Multiply $D$ by the next consecutive integer, $(D+1)$.\n3. Append '25' to the end of this product.\nWhy it works: $(10D+5)^2 = (10D)^2 + 2(10D)(5) + 5^2 = 100D^2 + 100D + 25 = 100D(D+1) + 25$. This shows you multiply $D(D+1)$ by 100 and add 25, which is exactly what 'appending 25' does!

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