How to Square Numbers in the 50s in Your Head
Square 51–59 by mixing 25 with the last digit.
= 2916
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54 × 54 is a square split at 50: 2500, 200, 200 and 16.
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Both middle pieces are 100 × 4, so the whole-hundred part is 100 × 29.
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So add the units digit to 25, then attach its square: .
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For 51 to 53 the square is one digit, so pad it: is written 04, and .
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.
Your turn
Three to try in your head. Tap what you get.
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All 36 shortcuts: the Magic Tricks library.