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Adding 2 Consecutive Square Numbers:
A. From algebra we know:
a2 + (a+1)2 = 2(a)(a+1) + 1
B. This
works for any consecutive squares. However if one of the squares is a
multiple of 5, the problem becomes very simple:
a2
+ (a+1)2 = 10
[(a)(a+1)] +
1
5
C. In
other words, the answer always ends in a 1. And you can divide one of the
numbers by 5 and multiply by the other to get the first part of the answer.
D.
Examples:
Ex [1] 352
+ 362 = _______
a. Write
down 1.
b. 35 ÷ 5 =
7. 7 x 36 = 252. Write 252.
c. The
answer is 2521.
Ex [2] 552
+ 542 = ________
a. Write
down 1.
b. 55 ÷ 5 =
11. 11 x 54 = 594. Write 594. See
Multiplying By 11.
c. The
answer is 5941.
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