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Math Help - question about radicals

  1. #1
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    question about radicals

    my question is this : Why is the sqrt[(2+sqrt(3))/4] = sqrt[2+sqrt(3)]/4 ?

    I thought it would be equal to sqrt[2+sqrt(3)]/2 but I saw the real answer. What am I doing wrong ? (im just taking the squareroot of the denominator. am I not supposed to do that?
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  2. #2
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    Quote Originally Posted by frankinaround View Post
    my question is this : Why is the sqrt[(2+sqrt(3))/4] = sqrt[2+sqrt(3)]/4 ?

    I thought it would be equal to sqrt[2+sqrt(3)]/2 but I saw the real answer. What am I doing wrong ? (im just taking the squareroot of the denominator. am I not supposed to do that?
    \displaystyle\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}=\f  rac{\sqrt{2+\sqrt{3}}}{\pm 2}

    Who said it was

    \displaystyle\frac{\sqrt{2+\sqrt{3}}}{4}\text{?}
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  3. #3
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    In short, it's not.

    \displaystyle \sqrt{\frac{2 + \sqrt{3}}{4}} = \frac{\sqrt{2 + \sqrt{3}}}{\sqrt{4}} = \frac{\sqrt{2 + \sqrt{3}}}{2} \neq \frac{\sqrt{2 + \sqrt{3}}}{4}.
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  4. #4
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    Quote Originally Posted by frankinaround View Post
    my question is this : Why is the sqrt[(2+sqrt(3))/4] = sqrt[2+sqrt(3)]/4 ?
    For the same reason 2 is equal to 4!!

    [I thought it would be equal to sqrt[2+sqrt(3)]/2 but I saw the real answer. What am I doing wrong ? (im just taking the squareroot of the denominator. am I not supposed to do that?
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