1. Sep 3, 2007

### davidavid

Hello friends,
I am studying in 10th class. Actually I have a question and I’m unable to solve this question. My question is: How can we find the square root of a number by hand? How about cube roots? If anybody can solve my question I will grateful. Thanks in advance!

2. Sep 3, 2007

### HallsofIvy

There are several methods, rather difficult to explain in this small area but here is a website that explains two:
http://www.homeschoolmath.net/teaching/square-root-algorithm.php

The first one is cute: on the face of it, it looks straight forward: to find $\sqrt{a}$ pick a starting number, x0, and divide it into a. If the quotient is larger than a, then the initial "guess", a0, is too small so pick x1 half way between x0 and a/x0[/sub]. Keep doing that, taking xn+1 = (xn+ a/xn)/2, until two succeeding value of x are the same to however many decimal places you want. It turns out that that method is what you get by applying "Newton's Method" to the f(x)= x2- a, but that may be deeper than you want to go.

3. Sep 3, 2007

### D H

Staff Emeritus
There is also an algorithm for extracting roots based on long division. A link: http://www.nist.gov/dads/HTML/squareRoot.html. This algorithm was taught extensively in schools before the advent of calculators.

4. Sep 3, 2007

### ryan_276

Hi,
I’m studying in 12th class. I can solve your question easily but I don’t have time for that so I would recommend you for a place called mindzinger where you can get any solution any time and regularly. I got it when was in 10th class. I used mindzinger and I got distinction in mathematics. It’s really nice place for getting solutions for all categories. Hope this will help you.
Good luck!

Last edited: Sep 3, 2007