secrets-of-mental-math-malestrom

The Tough Stuff Made Easy: Advanced Multiplication 177
FIVE-DIGIT SQUARES
Mastering 3-by-2 multiplication takes a fair amount of practice,
but once you’ve managed that, you can slide right into doing fivedigit
squares because they simplify into a 3-by-2 problem plus a
two-digit square and a three-digit square. Watch:
To square the following number:
Treat it as:
46,792 2
46,000 792
46,000 792
Using the distributive law we can break this down to:
1. 2. 3.
46,000 46,000 2(46,000)(792) 792 792
This can be stated more simply as:
46 2 1 million (46)(792)(2000) 792 2
But I do not do them in this order. In fact, I start in the middle,
because the 3-by-2 problems are harder than the two-digit
and three-digit squares. So in keeping with the principle of getting
the hard stuff out of the way first, I do 792 46 2 and
attach three zeroes on the end, as follows:
792
46
800 46 36,800
8 46 368
36,432
(800 8)
“Fisher”
2,000 72,864,000