Square Numbers Ending in 5 Instantly!

Ever need to quickly calculate $35^2$ or $85^2$ in your head? It sounds tricky, but there's a lightning-fast secret that makes it super easy!

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

The Trick

When squaring any number that ends in 5 (e.g., $N5$), follow two simple steps: \n1. Take the digit(s) before the 5 (let's call it $D$). Multiply $D$ by the next consecutive integer, $(D+1)$. \n2. Simply append the number $25$ to the result from step 1. That's your answer! \n\n**Why it works:** Any number ending in 5 can be written as $(10D+5)$. Squaring this gives $(10D+5)^2 = (10D)^2 + 2(10D)(5) + 5^2 = 100D^2 + 100D + 25 = 100D(D+1) + 25$. This shows the $D(D+1)$ part is multiplied by 100 (which is like appending two zeros), and then 25 is added.

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