Write an algorithm to find square of a number.
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Algorithm
Take a reasonable guess (approximate root) for the square root.
Add the approximate root with the original number divided by the approximate root and divide by 2. ...
Continue step 2 until the difference in the approximate root along the iterations is less than the desired value (or precision value).
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- Divide the number in two parts with one part containing only the number at unit's place say part 'A', and other part say 'B', containing the remaining number.
- Now square the number at unit's place. The square will be one of these; {0,1,4,9,16,25,36,49,64,81}. The unit's place digit in this square is the unit's place digit in actual final answer.Write it in the answer. If the square of digit at unit's place is a two digit no like from 16 to 81 in above set; write only the digit at unit's place from this square in the final answer and carry the remaining digit.
- Multiply the actual number to be squared by part 'B'(the remaining part than the number at unit's place as described in step 1 ).
- Multiply the parts 'A' and 'B'.
- Add results of step 3 with results of step 4.
- Add the carried digit from step 2 to the sum in prior step, that is step 5.
- Now write this sum before the number we wrote at unit's place of final answer in step 2.
- This number we now obtain from step 7, is the square of our number.
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