This has been covered in a recent thread at PF.Anukriti C. said:our maths teacher asked us that we all use the long division method to find square roots or cube roots. The question is, why do we do it that way, i.e. taking one or two nos. from the starting, doubling the divisor and all the steps(i guess everyone knows that). can anyone please help me and tell me the main objective or the actual reasons involved in each step?
thanks btw...actually I wanted to know why do we do it that way... I know how to do and what to do... I want to know how was it first derived?SteamKing said:This has been covered in a recent thread at PF.
Peruse this thread and see if some of the replies don't answer your question:
https://www.physicsforums.com/threa...oot-extraction-at-school.821407/#post-5157020
If there is anything you don't understand about the algorithm, post another question here and we'll try to clear it up for you.
This algorithm, and similar ones, have been developed at different times in the distant past.Anukriti C. said:thanks btw...actually I wanted to know why do we do it that way... I know how to do and what to do... I want to know how was it first derived?
Was it kinda hit and trial method or there is some logic behind it...
Not completely true. Computer square roots use this method, so square roots take the same amount of time as division.SteamKing said:With the development of logarithms, these algorithms became mathematical curiosities, at least for extracting roots in daily calculations.
It would be a mistake to assume that the algorithms used by computers for FP division and root extraction are merely hard-coded versions of the pen-and-paper procedures.mathman said:Not completely true. Computer square roots use this method, so square roots take the same amount of time as division.
The long division method is based on the concept of repeated subtraction. It involves breaking down a large number into smaller parts and dividing them by the divisor until there is no remainder left. This method is an extension of basic division and can be used to solve more complex division problems.
The long division method is used to solve division problems that cannot be easily solved using mental math or basic division. It allows for the division of large numbers and can be used to find precise decimal or fractional answers.
The steps involved in the long division method are:
1. Write the dividend (number being divided) on the left and the divisor (number dividing the dividend) on the outside.
2. Estimate the number of times the divisor can be subtracted from the first digit(s) of the dividend and write the quotient above the dividend.
3. Multiply the quotient by the divisor and write the product below the first digit(s) of the dividend.
4. Subtract the product from the first digit(s) of the dividend and write the difference below.
5. Bring down the next digit of the dividend and continue the process until there are no more digits to bring down.
6. If there is a remainder, it becomes the numerator of the fraction and the divisor becomes the denominator.
Some common mistakes to avoid when using the long division method are:
- Forgetting to bring down the next digit of the dividend
- Incorrectly estimating the number of times the divisor can be subtracted
- Making a mistake in the subtraction step
- Incorrectly placing the decimal point for decimal division
- Not checking the final answer for accuracy
The long division method can be applied in real-life situations such as:
- Calculating a restaurant bill when splitting the cost among a group of people
- Dividing a fixed amount of money among a certain number of people
- Calculating the cost per unit when buying items in bulk
- Converting units of measurement (e.g. inches to feet)
- Finding the average of a set of numbers
- Calculating interest or discounts on financial transactions