Squaring special numbers (4 and repeating 6’s)

Follow the following Steps:

  1. Choose a number with a 4 and repeating 6’s.
  2. The square is made up of:
    • first digits: 21 & one fewer 7 than repeating 6’s
    • next digits: 1 & one fewer 5 than repeating 6’s
    • last digit: 6

   Example:

  1. If the number to be squared is 4666:
  2. The square has:first digits: 21 and one fewer
        7 than 6's                   2 1 7 7
    next digits: 1 and one fewer
        5 than 6's                          1 5 5
    last digit: 6                                 6
  3. So 4666 × 4666 = 21,771,556.
   See the pattern?
  1. If the number to be squared is 466666:
  2. The square has:first digits: 21 and one fewer
       7 than 6's             2 1 7 7 7 7
    next digits: 1 and one fewer
       5 than 6's                        1 5 5 5 5
    last digit: 6                                  6
  3. So 466666 × 466666 = 217,777,155,556.