secrets-of-mental-math-malestrom

46
Secrets of Mental Math
41 2 1
42
1 40
1680 1 2 1681
To square 41, subtract 1 to obtain 40 and add 1 to obtain 42.
Next multiply 40 42. Don’t panic! This is simply a 2-by-1
multiplication problem (specifically, 4 42) in disguise. Since
4 42 168, 40 42 1680. Almost done! All you have to
add is the square of 1 (the number by which you went up and
down from 41), giving you 1680 1 1681.
Can squaring a two-digit number be this easy? Yes, with this
method and a little practice, it can. And it works whether you
initially round down or round up. For example, let’s examine
77 2 , working it out both by rounding up and by rounding down:
77 2 7
84
7 70
5880 7 2 5929
or
77 2 3
80
3 74
5920 3 2 5929
In this instance the advantage of rounding up is that you are
virtually done as soon as you have completed the multiplication
problem because it is simple to add 9 to a number ending in 0!
In fact, for all two-digit squares, I always round up or down
to the nearest multiple of 10. So if the number to be squared
ends in 6, 7, 8, or 9, round up, and if the number to be squared
ends in 1, 2, 3, or 4, round down. (If the number ends in 5, you