What is the trick of square of a number?

The Trick Behind Squaring Numbers Isn’t Magic—Just Math

Ever wondered if there’s a quicker way to square a number without reaching for a calculator? There’s a neat mental math trick, especially useful for numbers near 50 or those ending in 5.

Take squaring a number ending in 5, like 35. The trick? Multiply the first digit by the next number up, then attach 25 at the end. For 35², take the 3 and multiply it by 4 (the next number): 3 × 4 = 12. Then slap 25 on the end: 1225. So, 35² = 1,225. Quick, clean, and surprisingly satisfying.

Now, for numbers close to 50—say, 47—there’s another shortcut. Start with the base of 50² = 2,500. The difference between 50 and 47 is 3. Subtract twice this difference times 50, then add the square of the difference. That’s 2,500 – (2 × 3 × 50) + 3² = 2,500 – 300 + 9 = 2,209. So, 47² = 2,209. It’s not magic—it’s just smart use of algebra: (a – b)² = a² – 2ab + b².

You’ll also spot patterns elsewhere. For example, 40 × 41 = 1,640. Add 25? That’s 1,665—not a square, but the idea of attaching or adjusting by 25 shows up frequently with numbers ending in 5.

These shortcuts aren’t just party tricks. They reveal how numbers dance in patterns when you look closely. The “trick” isn’t a secret—it’s understanding relationships. Once you see that, squaring becomes less about memorization and more about playing with numbers.