There is a simple pattern in the following squares (as there was in the previous post for 100 to 110):
200 * 200 = 40000
201 * 201 = 40401
202 * 202 = 40804
203 * 203 = 41209
204 * 204 = 41616
205 * 205 = 42025
206 * 206 = 42436
207 * 207 = 42849
208 * 208 = 43264
209 * 209 = 43681
210 * 210 = 44100
Could you find it?
Here it is:
200 * 200 = (4 & 0000) + [(0 * 4) & 00] + (0^2) = 40000
201 * 201 = (4 & 0000) + [(1 * 4) & 00] + (1^2) = 40401
202 * 202 = (4 & 0000) + [(2 * 4) & 00] + (2^2) = 40804
203 * 203 = (4 & 0000) + [(3 * 4) & 00] + (3^2) = 41209
...
209 * 209 = (4 & 0000) + [(9 * 4) & 00] + (9^2) = 43681
210 * 210 = (4 & 0000) + [(10 * 4) & 00] + (10^2) = 44100
Example: To square 207 without a calculator or a pen, we add 7^2 to 7*4&00 and then add it to 4&0000; so it will be 42849 (in your mind imagine 42849 as 4,28,49; where 28=7*4 and 49=7^2).