There is a simple pattern in the following squares:
100 * 100 = 10000
101 * 101 = 10201
102 * 102 = 10404
103 * 103 = 10609
104 * 104 = 10816
105 * 105 = 11025
106 * 106 = 11236
107 * 107 = 11449
108 * 108 = 11664
109 * 109 = 11881
110 * 110 = 12100
Could you find it?
Here it is:
100 * 100 = (1 & 0000) + [(0 * 2) & 00] + (0^2) = 10000
101 * 101 = (1 & 0000) + [(1 * 2) & 00] + (1^2) = 10201
102 * 102 = (1 & 0000) + [(2 * 2) & 00] + (2^2) = 10404
103 * 103 = (1 & 0000) + [(3 * 2) & 00] + (3^2) = 10609
...
109 * 109 = (1 & 0000) + [(9 * 2) & 00] + (9^2) = 11881
110 * 110 = (1 & 0000) + [(10 * 2) & 00] + (10^2) = 12100
Example: To square 108 without a calculator or a pen, we add 8^2 to 8*2&00 and then add it to 1&0000; so it will be 11664 (in your mind imagine 11664 as 1,16,64; where 16=8*2 and 64=8^2).