Finding Square & Cube Roots by Hand

[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!

 

[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/x^{0[/sub]. Keep doing that, taking x_n+1 = (x_n+ a/x_n)/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.}

 

[D H]

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.

 

[ryan_276]

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!

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!