How to Square Numbers in the 40s in Your Head

Updated 4 October 2026

Square 41–49 by anchoring on 50.

$48^2$48² = 2304

How do you square a number in the 40s?

To square a number in the 40s, take its distance below 50 off 25, then attach the square of that distance as two digits. For 48², the distance is 2, so 25 − 2 = 23 and 2² = 4, written as 04, giving 2304. It works because 50² = 2500, and a number d below 50 has a square of 100 × (25 − d) + d²: the first part counts hundreds and the square of the distance fills the last two places. For 43², the distance is 7, so 25 − 7 = 18 and 7² = 49, giving 1849. For 41², the distance is 9, so 25 − 9 = 16 and 9² = 81, giving 1681. The same rule covers the 50s with the distance added: 53² gives 25 + 3 = 28 and 09, so 2809. Check the last digit: 48² must end in 4, because 8 × 8 = 64.

1. 48 is 2 below 50, so $48^2$48² is ${\left(50-2\right)}^2$(50 − 2)²: 2500 − 200 − 200 + 4.

2. Two lots of 100 × 2 come off the 2500, which leaves 100 × 23.

3. Take the distance off 25, then attach its square: $48^2=2304$48² = 2304.

All 36 shortcuts: the Magic Tricks library.