More squares in one line
The one-line algebra
Any number ending in 5 is (10n + 5). Squaring gives 100n² + 100n + 25 = 100×n(n+1) + 25. So n(n+1) forms the leading digits and 25 is always the last two digits — exactly the rule.
Two things to watch
- Using n instead of n(n+1). Multiply the tens part by the next whole number, not by itself.
- Dropping the 25. The answer always ends in 25 — never 05 or 20.
Square each number
Every answer ends in 25.
- 15²
- 45²
- 55²
- 75²
- 85²
- 105²
- 125²
- 25²
- 95²
- 65²
Good to know
Does this work for numbers like 105 or 235?
Yes. Take everything before the final 5 as n, compute n(n+1), and append 25. For 235: 23×24 = 552, so 235² = 55225.
Why does the answer always end in 25?
Because (10n+5)² = 100·n(n+1) + 25, the last two digits are fixed at 25 for every number ending in 5.
Vedic Maths — Veda Topper
Square Any Number Ending in 5 — Instantly
This is the trick that makes children gasp. To square 25, 35, 75 or 95 you do no long multiplication at all — you just multiply one small pair and stick 25 on the end. It uses the sutra Ekadhikena Purvena ("by one more than the one before").
The rule
To square a number ending in 5: take the digits before the 5, multiply them by one more than themselves, and write 25 after the result.
It works for bigger numbers too
Why it works
A number ending in 5 is (10n + 5). Squaring gives 100n² + 100n + 25 = 100 × n(n+1) + 25 — which is exactly "n times (n+1), then 25".
1) 45² 2) 55² 3) 85² 4) 125² 5) 65²
Answers: 1) 2025 2) 3025 3) 7225 4) 15625 5) 4225