Tutorial 66 |
Squaring numbers between 7000 and 7099
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- Choose a number between 7000 and 7099.
- The first three digits are: 4 9 0 _ _ _ _ _
- The next two digits are 4 times the last two digits,
with zero added: _ _ _ X X _ _
- For the last three digits, square the last two digits
in the number chosen (insert zeros when needed):
_ _ _ _ _ X X X
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Example:
- If the number to be squared is 7004:
- The first three digits are: 4 9 0 _ _ _ _ _
- The next two digits are 4 times the last two, with zero added:
4 × 4 = 16; 16 + 40 = 56: _ _ _ 5 6 _ _ _
- For the last three digits, square the last two:
4 × 4 = 16: _ _ _ _ 0 1 6
- So 7004 × 7004 = 49,056,016.
See the pattern?
For numbers greater than 7007, reverse the order:
- If the number to be squared is 7025:
- For the last three digits, square the last two:
25 × 25 = 625: _ _ _ _ 6 2 5
- 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 _ _ _
- The first three digits are 490 + the carry:
490 + 3 = 493: 4 9 3 _ _ _ _ _
- So 7025 × 7025 = 49,350,625.
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