228 Appendix J
Why does it work? Try using 70 as a reference number and you will
see we are dealing with something we already know.
+5
+5
70 75 × 75 = 80
5,600
- 25
5,625
Try the problem for yourself using 80 as a reference number. It
works out the same.
So for 135^2 (135 × 135) the front part of the number is 13 (in front
of the 5). We add 1 to get 14. Now multiply 13 × 14 = 182 (using
the shortcut in Chapter 3).
We square 5, or just put 25 at the end of our answer.
1352 = 18,225
For that we used either 130 or 140 as a reference number.
Try squaring 965 in your head.
Ninety-six is in front of the 5.
96 + 1 = 97
96 × 97 = 9,312
Put 25 at the end for the answer.
9652 = 931,225
Th at is really impressive.
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