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Thread: solution without calculator

  1. #1
    May 2012
    South Yorkshire

    solution without calculator

    Hello, I am new to this forum and was wondering if someone would be able to give me some help with an equation please. I am trying to workout the solution to the following problem without the use of a calculator. Any help would be greatfully appreciated.
    solution without calculator-equation.png
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  2. #2
    MHF Contributor

    Apr 2005

    Re: solution without calculator

    Some parts of that are easy- \sqrt{36}= 6 so the numerator of that fraction is 6- 5/2= 7/2. The denominator is a little harder.
    The 1/4 root is the "squareroot of the square root". There is an algorithm for taking the square root similar to "long division" but I prer an iterative method: We know that 1/2 squared is 1/4 which is too small and 1 squared is 1 which is too large- so try a number in between 1/2 and 1- and just to make it easy, try the number halfway between, (1+ 1/2)/2= 3/4. 3/4 squared is 9/16 which is which is less than 3/4= 12/16 so try the number half way between 3/4 and 1, 7/8. 7/8 squared is 49/64 which is just slightly larger than 3/4 so try half way between 7/8 and 3/4, 13/16. Keep doing that until you get a number whose square is close enough to 3/4. Then do the same thing with that number to find a number whose square is close enough to [b]that[b]. The result will be the fourth root of 3/4. Once you have that, divide it into 7/2. Call that result "A". Now you need to find the 3/2 power of A. Cubing A is easy. To find the 3/2 power of A, find the square root of A^3 using that same procedure: choose any starting number, x, and divide A by x to get "y". Choose your next trial "x" to be half way between the old x and y and repeat.
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