Tutorial 61 |
Squaring numbers between 2000 and 2099
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- Choose a number between 2000 and 2099. (Start with numbers below 2025
to begin with, then graduate to larger numbers.)
- The first two digits are: 4 0 _ _ _ _ _
- The next two digits are 4 times the last two digits:
4 0 X X _ _ _
- For the last three digits, square the last two digits
in the number chosen (insert zeros when needed):
4 0 _ _ X X X
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Example:
- If the number to be squared is 2003:
- The first two digits are: 4 0 _ _ _ _ _
- The next two digits are 4 times the last two:
4 × 3 = 12: _ _ 1 2 _ _ _
- For the last three digits, square the last two:
3 × 3 = 9: _ _ _ _ 0 0 9
- So 2003 × 2003 = 4,012,009.
See the pattern?
For larger numbers, reverse the order:
- If the number to be squared is 2025:
- For the last three digits, square the last two:
25 × 25 = 625: _ _ _ _ 6 2 5
- The middle two digits are 4 times the last two (keep the carry):
4 × 25 = 100 (keep carry of 1): _ _ 0 0 _ _ _
- The first two digits are 40 + the carry:
40 + 1 = 41: 4 1 _ _ _ _ _
- So 2025 × 2025 = 4,100,625.
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