How to Square Numbers in the 50s in Your Head

Updated 4 October 2026

Square 51–59 by mixing 25 with the last digit.

$54^2$54² = 2916

How do you square a number in the 50s?

To square a number in the 50s, add its units digit to 25, then attach the square of that digit as two digits. For 54², the units digit is 4, so 25 + 4 = 29 and 4² = 16, giving 2916. It works because a number in the 50s is 50 + d, and its square is 2500 + 100d + d², which is 100 × (25 + d) + d². The square of the units digit is at most 81, so it always fits in the last two places. For 51 to 53, pad the square with a 0: 52² gives 27 and 04, so 2704. For 59², 25 + 9 = 34 and 9² = 81, giving 3481. The rule also runs down into the 40s, with the distance below 50 taken off instead: 47² gives 25 − 3 = 22 and 09, so 2209. Check the last digit: 59² must end in 1, because 9 × 9 = 81.

1. 54 × 54 is a square split at 50: 2500, 200, 200 and 16.

2. Both middle pieces are 100 × 4, so the whole-hundred part is 100 × 29.

3. So add the units digit to 25, then attach its square: $54^2=2916$54² = 2916.

4. For 51 to 53 the square is one digit, so pad it: $2^2=4$2² = 4 is written 04, and $52^2=2704$52² = 2704.

All 36 shortcuts: the Magic Tricks library.