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  1. #1
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    Help with square root without calculator

    873595

    I was not sure how to right this so i will also say it 87 radical 53595. I could do this with a calculator.
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    Quote Originally Posted by MistaMista View Post
    873595

    I was not sure how to right this so i will also say it 87 radical 53595. I could do this with a calculator.
    First simplify a bit: 87\sqrt{53595} = 87\sqrt{9\cdot5955} = 261\sqrt{5955}

    Now, there are many methods you could use to obtain a numerical approximation of \sqrt{5955}.

    If you know calculus, you can use the Newton-Raphson method to find the zeros of the equation x^2 - 5955 = 0.

    Alternatively, try the Babylonian method: For \sqrt{S},
    1. Choose an arbitrary positive start value x_0 (try to pick one close to the root).
    2. Let x_{n+1} be the average of x_n and \frac S{x_n}, i.e. x_{n+1} = \frac12\left(x_n + \frac S{x_n}\right).
    3. Repeat steps 2 and 3 until you reach the desired accuracy.
    When choosing your initial value, 77 makes a good choice: 77^2 = 5929 < 5955 < 78^2 = 6084. Good luck!
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by MistaMista View Post
    873595

    I was not sure how to right this so i will also say it 87 radical 53595. I could do this with a calculator.

    The best manual method I have found is discussed here: How to Find Square Roots Without a Calculator - by E. Oosterwal

    It is much like long division. Follow the example given. Then try your radical. It's really quite simple. No guess work involved.
    Attached Thumbnails Attached Thumbnails Help with square root without calculator-square-root.bmp  
    Last edited by masters; July 2nd 2008 at 12:12 PM.
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