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Thread: Please Help Me!

  1. #1
    daniel_dan
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    Please Help Me!

    Hello friends,
    I am studying in 10th class. Actually I have a question and Iím 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!
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  2. #2
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    Quote Originally Posted by daniel_dan View Post
    Hello friends,
    I am studying in 10th class. Actually I have a question and Iím unable to solve this question. My question is: How can we find the square root of a number by hand?
    I am going to give an an algorithmic approach. Meaning a step-by-step program to do by hand. Each time you do a step the better you get to the square root.

    Let $\displaystyle x$ be some positive number. And we want to find $\displaystyle \sqrt{x}$. Let $\displaystyle a$ be your guess. Meaning what you think the square root it. You can be totally off, it will still work. But the better you guess the faster it will work.

    Find $\displaystyle \frac{a^2 + x }{2a}$.
    Call this $\displaystyle b$.

    Now pretend that $\displaystyle b$ is your guess. (Which is now better).
    Find,
    $\displaystyle \frac{b^2+x}{2b}$.
    Call this $\displaystyle c$.

    Now this is $\displaystyle c$ is better so find $\displaystyle \frac{c^2+x}{2c}$. And keep on going .... The more you do it the closer you get.

    For example, you want to find $\displaystyle \sqrt{2}$.

    Make a guess $\displaystyle a=1$.

    That means $\displaystyle b = \frac{1^2 + 2}{2(1)} =1.5$.

    That means $\displaystyle c=\frac{1.5^2 + 2}{2(1.5)} = 1.41$.

    You can see you start getting better and better.
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  3. #3
    zachary
    Guest

    Re: Please Help Me!

    Hi,
    Iím studying in 12th class. I can solve your question easily but I donít 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. Itís really nice place for getting solutions for all categories. Hope this will help you.
    Good luck!
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