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Math Help - Can you convert a decimal to a radical in simplest form?

  1. #1
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    Can you convert a decimal to a radical in simplest form?

    Hello,

    Can you help me find how to convert a decimal number to a radical (not rational) in simplest form? I need the answer with the check mark in it. ;^) For example, 3(check mark)5 = 6.70820394. But, how do you get that in reverse if you only know the decimal answer?

    Otherwise, do you know of an online calculator or solver, or something like the TI-83 Graphing Calculator that would convert this?

    Thanks,
    Dan

    PS
    This seems to be essential for pre-calc, calc, and trig problems, but I haven't found an answer after several hours of searching on the Internet. Thanks for the help.
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  2. #2
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    Quote Originally Posted by dschutte View Post
    Hello,

    Can you help me find how to convert a decimal number to a radical (not rational) in simplest form? I need the answer with the check mark in it. ;^) For example, 3(check mark)5 = 6.70820394. But, how do you get that in reverse if you only know the decimal answer?

    Otherwise, do you know of an online calculator or solver, or something like the TI-83 Graphing Calculator that would convert this?

    Thanks,
    Dan

    PS
    This seems to be essential for pre-calc, calc, and trig problems, but I haven't found an answer after several hours of searching on the Internet. Thanks for the help.
    What does "3(check mark)5" mean?
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  3. #3
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    It's 3(square root symbol, aka radical)5.
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  4. #4
    Super Member malaygoel's Avatar
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    simply square the decimal expression....you will get an integer.

    In you example, you will get 45...so the radical experssion will be
    \sqrt{45}=\sqrt{3^25}=3\sqrt{5}

    if the square is...say 120...then the radical expression will be
    \sqrt{120}=\sqrt{2^230}=2\sqrt{30}
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  5. #5
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    Thanks Malay. Wow, that's actually really simple. When I Googled my question, others where asking also, but no seemed to know how to explain a simple answer. You rock, thanks a million!!
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  6. #6
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    note that this technique of squaring only works if the decimal representation was calculated from the square root function of the calculator.

    just typing in the decimal representation and squaring will, at best, get you a number close to an integer if the square root is irrational.

    of course, it also helps to know that the decimal is the result of a square root ... could be a cube, fourth, fifth root ... etc.
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by dschutte View Post
    Hello,

    Can you help me find how to convert a decimal number to a radical (not rational) in simplest form? I need the answer with the check mark in it. ;^) For example, 3(check mark)5 = 6.70820394. But, how do you get that in reverse if you only know the decimal answer?

    Otherwise, do you know of an online calculator or solver, or something like the TI-83 Graphing Calculator that would convert this?

    Thanks,
    Dan

    PS
    This seems to be essential for pre-calc, calc, and trig problems, but I haven't found an answer after several hours of searching on the Internet. Thanks for the help.
    3\sqrt{5} = 6.70820394

    is incorrectly rounded.

    Removing the last digit (or correcting it) and feeding the number into the inverse symbolic calculator gives:



    CB
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  8. #8
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    Thanks Captain Black! I think that "Inverse Calculator" might be just the thing I've been searching for. I found it at http://glooscap.cs.dal.ca:8087/standard
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