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Math Help - Help me solve the square root of a square root.

  1. #1
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    Help me solve the square root of a square root.

    Here's an image of my problem.
    Attached Thumbnails Attached Thumbnails Help me solve the square root of a square root.-squarroot.gif  
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  2. #2
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    Quote Originally Posted by coopsterdude
    Here's an image of my problem.
    Hello,

    there are a few different ways to simplify this term:

    \sqrt{12 \cdot \sqrt{3}}=\sqrt{ \sqrt{12^2 \cdot3}}= \sqrt[4]{432}

    or:

    \sqrt{12 \cdot \sqrt{3}}=\sqrt{2^2 \cdot 3 \cdot \sqrt{\cdot3}}= 2 \cdot \sqrt{\sqrt{3^2 \cdot 3}}=2 \cdot \sqrt[4]{27}

    Greetings

    EB
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  3. #3
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    ... or \sqrt{12\sqrt{3}} = (12(3^{1/2}))^{1/2} = (12)^{1/2}((3)^{1/2})^{1/2} = (2^2.3)^{1/2} 3^{1/4} = (2^2)^{1/2} 3^{1/2+1/4} = 2.3^{3/4} = 2\sqrt[4]{27}.
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