Tutorial 65 |
Squaring numbers between 6000 and 6099
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- Choose a number between 6000 and 6099.
- The first three digits are: 3 6 0 _ _ _ _ _
- The next two digits are 12 times the last two digits:
_ _ _ 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 6004:
- The first three digits are: 3 6 0 _ _ _ _ _
- The next two digits are 12 times the last two:
12 × 4 = 48: _ _ _ 4 8 _ _ _
- For the last three digits, square the last two:
4 × 4 = 16: _ _ _ _ 0 1 6
- So 6004 × 6004 = 36,048,016.
See the pattern?
For numbers greater than 6008, reverse the order:
- If the number to be squared is 6020:
- For the last three digits, square the last two:
20 × 20 = 400: _ _ _ _ 4 0 0
- The middle two digits are 12 times the last two:
12 × 20 = 240 (keep carry): _ _ _ 4 0 _ _ _
- The first digits are 360 + the carry:
360 + 2 = 362: 3 6 2 _ _ _ _ _
- So 3025 × 3025 = 36,240,400.
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