Squaring Two-Digit Numbers
💡 How to solve ▾
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.
A worked example
35²: take 3 × 4 = 12 and append 25 to get 1225. For 41²: 40² = 1600, plus 40 + 41 = 81, gives 1681.
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.