Tutorial 64 |
Squaring numbers between 5000 and 5099
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- Choose a number between 5000 and 5099.
- The first three digits are: 2 5 0 _ _ _ _ _
- The next two digits are 10 times the last two digits:
2 5 0 X X _ _ _
- For the last three digits, square the last two digits
in the number chosen (insert zeros when needed):
2 5 0 _ _ X X X
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Example:
- If the number to be squared is 5004:
- The first three digits are: 2 5 0 _ _ _ _ _
- The next two digits are 10 times the last two:
10 × 4 = 40: _ _ 4 0 _ _ _
- For the last three digits, square the last two:
4 × 4 = 16: _ _ _ _ _ 0 1 6
- So 5004 × 5004 = 25,040,016.
See the pattern?
For numbers greater than 5011, reverse the order:
- If the number to be squared is 5012:
- For the last three digits, square the last two:
12 × 12 = 144: _ _ _ _ 1 4 4
- The middle two digits are 10 times the last two (keep the carry):
10 × 12 = 120 (keep carry of 1):
_ _ _ 2 0 _ _ _
- The first three digits are 150 + the carry:
250 + 1 = 251: 2 5 1 _ _ _ _ _
- So 5012 × 5012 = 25,120,144.
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