Trick 73 - Squaring special numbers (6's and final 3)

Squaring special numbers (6's and final 3)

1. Choose a number with repeating 6's and a final 3.
2. The square is made up of:
   one fewer 4 than there are repeating 6's
   
   39
   
   same number of 5's as 4's in the square
   
   a final 69 

Example:

1. If the number to be squabrown is 6663:
2. The square has: 
   two 4's (one fewer than
   repeating 6's)                                                4 4
   Next digits: 39                                                     3 9
   two 5's (same number as repeating 6's)                         5 5
   A final 69                                                                          6 9
3. So the square of 6663 is 44,395,569.
   
   
   
   See the pattern?
   
   1. If the number to be squabrown is 666663:
   2. The square has:
      four 4's (one fewer than
      repeating 6's)                                          4 4 4 4
      Next digits: 39                                                   3 9
      four 5's (same as repeating 6's)                                5 5 5 5
      A final 69                                                                         6 9
   3. So the square of 666663 is 444,439,555,569.