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Math Help - Radicals #6

  1. #1
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    Post Radicals #6

    imgur: the simple image sharer

    I am having a tough time simplifying radicals after I multiply... Any help would be great, I already know the answer; I need to understand though, my textbook is not clear enough for me.

    In the picture, you will see I wrote the answer down, but I couldn't finish my work because I did not know how.
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  2. #2
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    Re: Radicals #6

    it is c) e) and f)
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  3. #3
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    Re: Radicals #6

    It is very difficult to read what you have written. Is what looks like 2^4\sqrt{48} supposed to be 2\sqrt[4]{48}?
    If so then the problem is to write 2\sqrt[4]{48}\times \sqrt[4]{5} in the simplest form. The easiest way to do this, especially if you have "a tough time simplifying radicals after I multiply" is to simplify the radicals before you multiply. Here, recognise that 48= 2(24)= 2(2)(12)= 2(2)(2)(6)= 2(2)(2)(2)(2)(3) which is 2^4(3) so that \sqrt[4]{48}= 2\sqrt[4]{3}. So 2\sqrt{48}\times \sqrt[4]{5}= 2(2\sqrt[4]{3})(\sqrt[4]{5})= 4\sqrt{15}

    In (e), is that \sqrt[3]{54 y^7}\times \sqrt[3]{6y^4}? 3 divides into 7 twice with remainder 1 so y^7= (y^3)(y^3)y so \sqrt[3]{y^7}= y^2\sqrt[3]{y}. 54= (27)(2) and 27= 3^3 so \sqrt[3]{54}= 3\sqrt[3]{2} and \sqrt[3]{54y^7}= 3y^2\sqrt{2y}. Of course, y^4= y^3(y) while 6= 2(3) does not have any "cubes" so \sqrt[3]{6y^4}= y\sqrt[3]{6y}. So \sqrt[3]{54y^7}\times\sqrt[3]{6y^4}= \left(3y^2\sqrt[3]{2y}\right)\left(y\sqrt{6y}\rignt)= 2y^3\sqrt[3]{12y^2}.
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    Re: Radicals #6

    f?
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  5. #5
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    Re: Radicals #6

    I'll post it here, though it also applies to #7. As HallsofIvy pointed out there is a problem with your notation. For example in f), what is under the radical in the first term. It looks like
    \sqrt{6}t \left ( 3t^2 \sqrt{\frac{t}{4}} \right )

    or
    \sqrt{6t} \left ( 3t^2 \frac{\sqrt{t}}{4} \right )

    or something else? Could you please insert some parenthesis in there?

    -Dan
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  6. #6
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    Re: Radicals #6

    It is the first one; how do you guys type like that?
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    Forum Admin topsquark's Avatar
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    Re: Radicals #6

    Check out the LaTeX forum.

    -Dan
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  8. #8
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    Re: Radicals #6

    So, I don't know how to do f), do I multiply 6 by t and 4 in the other bracket to get 6t^2 and 24?
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