secrets-of-mental-math-malestrom

74
Secrets of Mental Math
2. The easy way: double the number 63 to get 126, and take the last
two digits to give you 826.
Here’s why the easy way works. Because both numbers are
the same distance from 863, their sum must be twice 863, or
1726. One of your numbers is 900, so the other must be 826.
You then compute the problem like this:
37 900
863 2 743,400 37 2 744,769
37
826
3
40
37 2 1,360 3 2 1,369
3
34
If you find it impossible to remember 743,400 after squaring
37, fear not. In a later chapter, you will learn a memory system
that will make remembering such numbers much easier.
Try your hand at squaring 359, the hardest problem yet:
41 400
359 2 127,200 41 2 128,881
41
318
1
42
41 2 1,680 1 2 1,681
1
40
To obtain 318, either subtract 41 (the complement of 59)
from 359, or multiply 2 59 118 and use the last two digits.
Next multiply 400 318 127,200. Adding 41 2 , or 1,681,
gives you 128,881. Whew! They don’t get much harder than
that! If you got it right the first time, take a bow!
Let’s finish this section with a big problem that is easy to
do, 987 2 :