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What is the square route of 99???
  • Its a method to find root Algebraically

    SQRT(99) is an irrational, approximately equal to 9.95.
    [I bet you already knew that it was just a little less than 10]



    Here's how I came up with 9.95 without using a calculator:



    Since 10^2 = 100,

    Therefore,SQRT(99) must be 10-d where d is much smaller than 1.

    A little algebra:

    (10-d)*(10-d)=99

    100-20*d+d*d =99

    1-20*d+d*d = 0

    1-20*d = -d*d,

    but d << 1 (much smaller than),so d*d is even less

    and for a good approximation, we can assume it's 0:

    1-20*d ~= 0

    d = 1/20 = 0.05


    The actual value of SQRT(99) is 9.94987, so our approximation is pretty good.
  • 2 Comments sorted by
  • hey its great!!! ur absolutely correct!!!

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