The 'Ends in 5' Squaring Secret!

Ever wished you could square big numbers like 35 or 75 in your head, super fast? ✨ Get ready to amaze yourself and your friends with this neat trick!

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

The Trick

To square any number ending in 5, follow these steps: 1. Take the digit(s) before the 5. Let this be 'a'. 2. Multiply 'a' by $(a+1)$. 3. Append '25' to the result. That's it! Why it works: Consider a number $(10a + 5)$. Its square is $(10a + 5)^2 = (10a)^2 + 2(10a)(5) + 5^2 = 100a^2 + 100a + 25 = 100a(a+1) + 25$. This means the first part of the answer is $a(a+1)$ multiplied by 100 (which shifts it two places left), and 25 is added on.

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