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Math Help - simplifying radicals

  1. #1
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    simplifying radicals

    forgive me but i dont know how to do this in Latex

    cubed root(-81xcubed) - 2x cubed root(3) + 5x cubed root(24)

    i dont need to solve i just need to simplify.
    I think i have some idea like for cubed root 81 do i find a smaller number cubed to take out? what?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by MistaMista View Post
    forgive me but i dont know how to do this in Latex

    cubed root(-81xcubed) - 2x cubed root(3) + 5x cubed root(24)

    i dont need to solve i just need to simplify.
    I think i have some idea like for cubed root 81 do i find a smaller number cubed to take out? what?
    That's ok, in LaTeX, this would be:

    Code:
    \sqrt[3]{-81x^3}-2x\sqrt[3]{3}+5x\sqrt[3]{24}
    Be sure to put the code in the "math" tags

    \sqrt[3]{-81x^3}-2x\sqrt[3]{3}+5x\sqrt[3]{24}

    Simplifying, we get

    \sqrt[3]{(-3)^3x^3}-2\sqrt[3]{3}x+5x\sqrt[3]{2^3\times 3}

    \implies -3x-2\sqrt[3]{3}x+5x(2\sqrt[3]{3})

    \implies (-3-2\sqrt[3]{3}+10\sqrt[3]{3})x

    \implies\color{blue}\boxed{(-3+8\sqrt[3]{3})x}

    Does this makes sense?

    --Chris
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  3. #3
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    no sense

    Can you explain how you did this b/c i am wondering how your moving from step to step
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  4. #4
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    Hello, MistaMista!

    \sqrt[3]{-81x^3} - 2x\sqrt[3]{3} + 5x\sqrt[3]{24}

    I think i have some idea like for \sqrt[3]{81}
    Do i find a smaller number cubed to take out? . . . . Yes!

    The first term is: . \sqrt[3]{-81x^3} \:=\:\sqrt[3]{(-27)(3)x^3} \:=\:\sqrt[3]{-27}\!\cdot\!\sqrt[3]{3}\!\cdot\!\sqrt[3]{x^3} \;=\;-3x\sqrt[3]{3}

    The last term is: . 5x\sqrt[3]{24} \;=\;5x\sqrt[3]{(8)(3)} \;=\;5x\sqrt[3]{8}\!\cdot\!\sqrt[3]{3}\;=\;5x\!\cdot\!2\sqrt[3]{3} \;=\;10x\sqrt[3]{3}


    The problem becomes: . -3x\sqrt[3]{3} - 2x\sqrt[3]{3} + 10x\sqrt[3]{3}

    They are all "similar" terms: . (-3-2+10)x\sqrt[3]{3} \;\;=\;\;\boxed{5x\sqrt[3]{3}}

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  5. #5
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    thanks

    i think its just going to take me some time to get it.
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, MistaMista!


    The first term is: . \sqrt[3]{-81x^3} \:=\:\sqrt[3]{(-27)(3)x^3} \:=\:\sqrt[3]{-27}\!\cdot\!\sqrt[3]{3}\!\cdot\!\sqrt[3]{x^3} \;=\;-3x\sqrt[3]{3}

    The last term is: . 5x\sqrt[3]{24} \;=\;5x\sqrt[3]{(8)(3)} \;=\;5x\sqrt[3]{8}\!\cdot\!\sqrt[3]{3}\;=\;5x\!\cdot\!2\sqrt[3]{3} \;=\;10x\sqrt[3]{3}


    The problem becomes: . -3x\sqrt[3]{3} - 2x\sqrt[3]{3} + 10x\sqrt[3]{3}

    They are all "similar" terms: . (-3-2+10)x\sqrt[3]{3} \;\;=\;\;\boxed{5x\sqrt[3]{3}}

    Forgot that 3^4=81, \ not \ 3^3=81...
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  7. #7
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    i get it nows

    ok i understand. i was looking at it in the wrong way. Thanks a lot
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