Squaring Numbers Ending in 5 - Lightning Fast!

Ever need to square a number like 35 or 75 quickly in your head? Forget long multiplication! There's a trick that makes it feel like magic!

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

The Trick

For any number ending in $5$, say $N5$ (where $N$ is the digit(s) before $5$), its square will always end in $25$. To find the digits preceding $25$, simply multiply $N$ by the next consecutive integer, $(N+1)$. So, $(N5)^2 = (N \times (N+1))25$. \n\n*Why it works?* Let the number be $10N+5$. $(10N+5)^2 = (10N)^2 + 2(10N)(5) + 5^2 = 100N^2 + 100N + 25 = 100(N^2+N) + 25 = 100(N(N+1)) + 25$. This clearly shows $N(N+1)$ in the hundreds place and above, followed by $25$.

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