Squaring special numbers (9’s and final 3)

Follow the following Steps:

  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 × 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 × 999993 = 999986000049.