How to Square Numbers Near 1000 in Your Head
Square numbers near 1000 by anchoring on 1000.
= 992016
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996 sits 4 below 1000, so is .
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The distance comes off twice: 1000 − 2 × 4 is 992, or just 996 − 4.
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Then attach , padded to three digits because the anchor has three zeros.
How do you square a number near 1000?
To square a number near 1000, take its distance from 1000 off the number, then attach the square of that distance as three digits. For 996², the distance is 4, so 996 − 4 = 992 and 4² = 16, written as 016, giving 996² = 992016.
It works because (1000 − d)² is 1000 × (1000 − 2d) + d², so the first part counts thousands and the square of the distance fills the last three places.
A number just above 1000 takes the distance added instead: 1007 is 7 above, so 1007 + 7 = 1014 and 7² = 49, written as 049, giving 1014049. From a distance of 32 onward, the square has four digits and carries into the thousands: 965 is 35 below 1000, so 965 − 35 = 930 and 35² = 1225, giving 965² = 930000 + 1225 = 931225. Check the last three digits first, because they always match the last three digits of the distance squared.
Your turn
Three to try in your head. Tap what you get.
= ?
= ?
= ?
All 36 shortcuts: the Magic Tricks library.