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Math Help - Confusion with a particular surd simplification

  1. #1
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    Confusion with a particular surd simplification

    Hey guys, I'm stuck bad on this simplification:

    \sqrt{201-\sqrt{401}} = \frac{\sqrt{401}-1}{\sqrt{2}}

    I'd highly appreciate a swift response.

    Thanks guys!
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  2. #2
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    Re: Confusion with a particular surd simplification

    Quote Originally Posted by Code2004 View Post
    Hey guys, I'm stuck bad on this simplification:

    \sqrt{201-\sqrt{401}} = \frac{\sqrt{401}-1}{\sqrt{2}}

    I'd highly appreciate a swift response.

    Thanks guys!
    \displaystyle \begin{align*} x &= \frac{\sqrt{401} - 1}{\sqrt{2}} \\ \sqrt{2}\,x &= \sqrt{401} - 1 \\ \left( \sqrt{2}\,x \right)^2 &= \left( \sqrt{401} - 1 \right)^2 \\ 2x^2 &= 401 - 2\sqrt{401} + 1 \\ 2x^2 - 402 &= -2\sqrt{401} \\ x^2 - 201 &= -\sqrt{401} \\ x^2 &= 201 - \sqrt{401} \\ x&= \sqrt{201 - \sqrt{401}}  \end{align*}

    So clearly \displaystyle \begin{align*} \frac{\sqrt{401} - 1}{\sqrt{2}} = \sqrt{201 - \sqrt{401}} \end{align*}.
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  3. #3
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    Re: Confusion with a particular surd simplification

    Of course, excellent. Thanks!
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