Square 47 in your head

Question

Solve in your head, no written work. What is 47^2? Aim: under 6 seconds.

Accepted Answer

The handy anchor here is 50, not 100: 47 = 50 - 3, so 47^2 = (50 - 3)^2 = 2500 - 300 + 9 = 2209. The middle term is 2 	imes 50 	imes 3 = 300; the last is 3^2 = 9. Alternative via the slide trick: n^2 = (n - d)(n + d) + d^2 with d = 3 gives 47^2 = 44 	imes 50 + 9 = 2200 + 9 = 2209. Since 44 	imes 50 = 44 	imes 100 / 2 = 2200, this is quick. Takeaway. Anchor to the nearest convenient round number, which may be 50 (or 25, 500, etc.), not just powers of ten. E.g. 53^2 = 56 	imes 50 + 9 = 2809, and 48^2 = 46 	imes 50 + 4 = 2304.

Square 47 in your head

Your answer

More Mental Math questions