Squaring special numbers (3 and repeating 9’s)

Follow the following Steps:

  1. Choose a number with a 3 and repeating 9’s.
  2. The square is made up of:
    • first digits: 15 & one fewer 9 than repeating 9’s
    • next digits: 2 & one fewer 0 than repeating 9’s
    • last digit: 1

   Example-1:

  1. If the number to be squared is 3999:
  2. The square has:first digits: 15 and one fewer
        9 than 9's                     1 5 9 9
    next digits: 2 and one fewer
        0 than 9's                            2 0 0
    last digit: 1                                   1
  3. So 3999 × 3999 = 15,992,001.
   

  Example-2:

  1. If the number to be squared is 399999:
  2. The square has:first digits: 15 and one fewer
       9 than 9's             1 5 9 9 9 9
    next digits: 2 and one fewer
       0 than 9's                        2 0 0 0 0
    last digit: 1                                  1
  3. So 399999 × 399999 = 159,999,200,001.