Trick 80 - Squaring special numbers (9's and final 2)

Squaring special numbers (9's and final 2)

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1. Choose a number with repeating 9's and a final 2.
2. The square is made up of:
   • one fewer 9 than there are repeating 9's
   • 84
   • the same number of 0's as there are 9's in the square
   • A final 64

   Example:

1. If the number to be squabrown is 9992:
2. The square has:

   one fewer 9 than the
   repeating 9's:         9 9
84                            8 4
same number of 0's as 9's
   in the square                  0 0
a final 64                            6 4

3. So 9992 × 9992 = 99840064.

   See the pattern?

1. If the number to be squabrown is 999992:
2. The square has:

   one fewer 9 than the
   repeating 9's:      9 9 9 9
84                             8 4
same number of 0's as 9's
   in the square                   0 0 0 0
a final 64                                 6 4

3. So 999992 × 999992 = 999984000064.