Squaring Two-Digit Numbers
💡For a number ending in 5, multiply the tens digit by the next number up and stick 25 on the end. For others, round to a nearby ten and adjust.
Try it — square a two-digit number
liveNumbers ending in 5 have a one-step shortcut.
- 1
Take the tens digit times the next number up
3 × 4 = 12
- 2
Tack 25 on the end
12 → 1,225
⏱️ Practice against the clock
A worked example
35²: take 3 × 4 = 12 and append 25 to get 1225. For 41²: 40² = 1600, plus 40 + 41 = 81, gives 1681.
The “ends in 5” shortcut is not luck
Any number ending in 5 is 10a + 5. Square it and the algebra falls open: (10a+5)² = 100·a(a+1) + 25. The first part is always a times the next number up, counted in hundreds. The tail is always 25.
So 35² is 3 × 4 = 12, stick 25 on the end, 1225. No real multiplying involved. Same story for 85²: 8 × 9 = 72, then 25, giving 7225. Once you spot the pattern it is almost too easy.
For the rest, lean on a round neighbour
Round to the nearest ten, multiply that by its mirror on the far side of your number, then add the square of the gap. It is the old (n−d)(n+d) + d² identity quietly doing the work.
For 48²: the gap to 50 is 2, so 50 × 46 = 2300, plus 2² = 4, gives 2304. Multiplying by 50 is easy, and the little correction is a square you already know cold.
Questions people ask
Why does the "ends in 5" rule work? ▾
It falls out of the algebra of (10a + 5)². The tens part always produces a×(a+1) hundreds, and the 5² always contributes the trailing 25.
What is the trick for numbers near a round ten? ▾
Use the difference of squares idea: 48² = 50² − (2×50 − ... ). Simpler in practice: 48² = 50×46 + 2² = 2300 + 4 = 2304.