Tutorial 64
Squaring numbers between 5000 and 5099

  1. Choose a number between 5000 and 5099.
  2. The first three digits are: 2 5 0 _ _ _ _ _
  3. The next two digits are 10 times the last two digits:
    2 5 0 X X _ _ _
  4. For the last three digits, square the last two digits in the number chosen (insert zeros when needed):
    2 5 0 _ _ X X X

   Example:

  1. If the number to be squared is 5004:
  2. The first three digits are: 2 5 0 _ _ _ _ _
  3. The next two digits are 10 times the last two:
    10 × 4 = 40: _ _ 4 0 _ _ _
  4. For the last three digits, square the last two:
    4 × 4 = 16: _ _ _ _ _ 0 1 6
  5. So 5004 × 5004 = 25,040,016.

   See the pattern?

    For numbers greater than 5011, reverse the order:

  1. If the number to be squared is 5012:
  2. For the last three digits, square the last two:
    12 × 12 = 144: _ _ _ _ 1 4 4
  3. The middle two digits are 10 times the last two (keep the carry):
    10 × 12 = 120 (keep carry of 1):
    _ _ _ 2 0 _ _ _
  4. The first three digits are 150 + the carry:
    250 + 1 = 251: 2 5 1 _ _ _ _ _
  5. So 5012 × 5012 = 25,120,144.