Squaring special numbers (4 and repeating 3’s)

Follow the following Steps:

  1. Choose a number with a 4 and repeating 3’s.
  2. The square is made up of:
    • first digits: 18 & one fewer 7 than repeating 3’s
    • next digits: 4 & one fewer 8 than repeating 3’s
    • last digit: 9

   Example-1:

  1. If the number to be squared is 4333:
  2. The square has:first digits: 18 and one fewer
        7 than 3's                   1 8 7 7
    next digits: 4 and one fewer
        8 than 3's                          4 8 8
    last digit: 9                                 9
  3. So 4333 × 4333 = 18,774,889.
   

   Example-2:

  1. If the number to be squared is 433333:
  2. The square has:first digits: 18 and one fewer
       7 than 3's             1 8 7 7 7 7
    next digits: 4 and one fewer
       8 than 3's                        4 8 8 8 8
    last digit: 9                                  9
  3. So 433333 × 433333 = 187,777,488,889.