Squaring special numbers (9's and final 3)

1. Choose a number with repeating 9's and a final 3.
2. The square is made up of:
   • one fewer 9 than there are repeating 9's
   • 86
   • the same number of 0's as there are 9's in the square
   • A final 49

   Example:

1. If the number to be squared is 9993:
2. The square has:

   one fewer 9 than the
   repeating 9's:         9 9
86                            8 6
same number of 0's as 9's
   in the square                  0 0
a final 49                            4 9

3. So 9993 x 9993 = 99860049.

   See the pattern?

1. If the number to be squared is 999993:
2. The square has:

   one fewer 9 than the
   repeating 9's:      9 9 9 9
86                             8 6
same number of 0's as 9's
   in the square                   0 0 0 0
a final 49                                 4 9

3. So 999993 x 999993 = 999986000049.

Using this pattern you will be able to square these large numbers with ease.