n^2 = 10*k+r 0 < r < 9
r is the units (last) digit of a perfect square
Since
0²=0
1²=1,
2²=4,
3²=9
4²=16
5²=25
6²=36
7²=81
8²=64
9²=81
the last (units) digit of ALL perfect squares can
only be 0,1,4,5,6, or 9. Thus r can be
0,1,4,5,6, or 9, r cannot be 2,3,7, or 8.
02 = 10(0) + 0
12 = 10(0) + 1
22 = 10(0) + 4
32 = 10(0) + 9
42 = 10(1) + 6
52 = 10(2) + 5
62 = 10(3) + 6
72 = 10(4) + 9
Edwin