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Thread: square roots: best way to find roots of large numbers

  1. #1
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    square roots: best way to find roots of large numbers

    What is the best way to find the square root of a large number?

  2. #2
    Elite Member stapel's Avatar
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    That would depend, I suppose, upon the numbers and the tools available.

    Are you trying to find the square roots of large square numbers? Or just any numbers? Are you allowed to use calculators to find decimal approximations? Or are you finding "exact" answers? Or are you asking about "by hand" methods for finding decimal approximations?

    Please reply with the full and exact text of the exercise, the complete instructions, and a clear listing of what you have tried thus far.

    Thank you.

    Eliz.

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    square roots

    I need to find the square root of a large number, by hand, to the exact decimal. I was instructed to show the primary factorization and then use that to help me find the square root. How does the primary factorization help?

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    Elite Member stapel's Avatar
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    Quote Originally Posted by t-dog
    I need to find the square root of a large number, by hand, to the exact decimal.
    So you know that the number is the square of some other finite decimal number?

    (For instance, the square root 756.25 can be found "to the exact decimal", because 756.25 is 27.5<sup>2</sup>. But the square root of 756 cannot be found "to the exact decimal", because it isn't the square of a decimal. The number never terminates.)

    Quote Originally Posted by t-dog
    I was instructed to show the primary factorization and then use that to help me find the square root. How does the primary factorization help?
    If you're dealing with, as you say, a decimal, I don't see that it does, since decimals don't have prime factorizations. (Only whole numbers have prime factorizations, but then the square root would be a whole number, not a decimal.)

    I'm afraid the instructions you've received are self-contradictory. Either you're doing decimal root extraction by hand, or else you're using prime factorization to simplify whole-number root extraction. But I don't see how one could do both at the same time. Sorry.

    By the way, when you say that you're doing decimal-place roots by hand, are you asking for the "without a calculator" method for approximating roots? If so, there is an archived article explaining the method at Ask Dr. Math.

    Good luck!

    Eliz.

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