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## Squaring numbers between 1000 and 1100

Started by thiruvasagamani, Aug 18, 2008, 06:23 PM

#### thiruvasagamani

Squaring numbers between 1000 and 1100

1. Choose a number between 1000 and 1100.
2. The first two digits are: 1,0 _ _, _ _ _
3. Find the difference between your number and 1000.
4. Multiply the difference by 2: 1,0 X X, _ _ _
5. Square the difference: 1,0 _ _, X X X

Example:

1. If the number to be squared is 1007:
2. The first two digits are: 1,0 _ _, _ _ _
3. Find the difference: 1007 - 1000 = 7
4. Two times the difference: 2 × 7 = 14:
1,0 1 4, _ _ _
5. Square the difference: 7 × 7 = 49:
1,0 1 4, 0 4 9
6. So 1007 × 1007 = 1,014,049.

See the pattern?

1. If the number to be squared is 1012:
2. The first two digits are: 1,0 _ _, _ _ _
3. Find the difference: 1012 - 1000 = 12
4. Two times the difference: 2 × 12 = 24:
1,0 2 4, _ _ _
5. Square the difference: 12 × 12 = 144:
1,0 2 4, 1 4 4
6. So 1012 × 1012 = 1,024,144.

Start with lower numbers and then extend your expertise to all the numbers between 1000 and 1100. Remember to add the first digit as carry when the square of the difference is four digits.
Thiruvasakamani Karnan