The 'Ends in 5' Squaring Secret!

Ever wished you could square numbers like $35^2$ or $105^2$ in seconds, without a calculator? Unlock a lightning-fast mental math trick!

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

The Trick

When you need to square any number ending in 5, here's the magic: 1. Ignore the '5' for a moment and take the digit(s) before it. Let's call this number 'N'. 2. Multiply 'N' by ($N+1$). 3. Append '25' to the result of step 2. That's it! For example, for $35^2$, N=3. So, $3 \times (3+1) = 3 \times 4 = 12$. Append '25', so $1225$. **Why it works:** Let the number be $(10N+5)$. $(10N+5)^2 = (10N)^2 + 2(10N)(5) + 5^2$ $= 100N^2 + 100N + 25$ $= 100N(N+1) + 25$ This shows that you multiply $N(N+1)$ by 100 (which is effectively appending '00') and then add 25. So, you're essentially placing '25' after the result of $N(N+1)$. Neat, right?

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