Tutorial 66
Squaring numbers between 7000 and 7099

  1. Choose a number between 7000 and 7099.
  2. The first three digits are: 4 9 0 _ _ _ _ _
  3. The next two digits are 4 times the last two digits,
    with zero added: _ _ _ X X _ _
  4. For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
    _ _ _ _ _ X X X

   Example:

  1. If the number to be squared is 7004:
  2. The first three digits are: 4 9 0 _ _ _ _ _
  3. The next two digits are 4 times the last two, with zero added:
    4 × 4 = 16; 16 + 40 = 56: _ _ _ 5 6 _ _ _
  4. For the last three digits, square the last two:
    4 × 4 = 16: _ _ _ _ 0 1 6
  5. So 7004 × 7004 = 49,056,016.

   See the pattern?

    For numbers greater than 7007, reverse the order:

  1. If the number to be squared is 7025:
  2. For the last three digits, square the last two:
    25 × 25 = 625: _ _ _ _ 6 2 5
  3. For the middle two digits, add zero to the last two,
    then add 4 times the last two:
    250 + 4 × 25: 250 + 100 = 350 (keep carry):
    _ _ _ 5 0 _ _ _
  4. The first three digits are 490 + the carry:
    490 + 3 = 493: 4 9 3 _ _ _ _ _
  5. So 7025 × 7025 = 49,350,625.