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Math Help - Rationalize the denominator

  1. #1
    Senior Member Mukilab's Avatar
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    Rationalize the denominator

    Method and WIP please ^^

    \frac{1}{8\sqrt{8}}

    Give answer in the form \frac{\sqrt{2}}{p} Where p is a positive interger
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  2. #2
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    Quote Originally Posted by Mukilab View Post
    Method and WIP please ^^

    \frac{1}{8\sqrt{8}}

    Give answer in the form \frac{\sqrt{2}}{p} Where p is a positive interger
    \frac{1}{8\sqrt{8}} = \frac{1}{8\cdot 2 \sqrt{2}} = \frac{1}{8\cdot 2 \sqrt{2}}\cdot \  \color{red}\frac{\sqrt{2}}{\sqrt{2}}

    And now it's your turn.
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  3. #3
    Senior Member Mukilab's Avatar
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    Yes it is. How did you get 8*2\sqrt2?

    Method for that

    and from that step how did you get to the two square routes of 2? Method for that too please
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Mukilab View Post
    Yes it is. How did you get 8*2\sqrt2?

    Method for that

    and from that step how did you get to the two square routes of 2? Method for that too please
    For \sqrt{8} = 2\sqrt{2} you need to know that \sqrt{a^2} = a and \sqrt{ab} = \sqrt{a}\sqrt{b}

    8 = 2^3 = 2^2 \cdot 2

    \sqrt{8} = \sqrt{2^2 \cdot 2} = \sqrt{2^2} \cdot \sqrt{2} = 2\sqrt{2}

    ---------------------------------

    The \frac{\sqrt{2}}{\sqrt{2}} comes about because we can multiply a fraction by 1 and leave it unchanged.

    \frac{\sqrt{2}}{\sqrt{2}} = 1
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  5. #5
    Senior Member Mukilab's Avatar
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    so \frac{1}{8\cdot 2\sqrt{2}}=\frac{1}{2^{4}\sqrt{2}}???


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  6. #6
    MHF Contributor
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    Yes, but that is not the form requested, Mukilab.
    Look at Earboth's solution.
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  7. #7
    Senior Member Mukilab's Avatar
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    But I don't get how this

    Goes to


    Wait. Is that even the answer? I'm confused.
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  8. #8
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Mukilab View Post
    But I don't get how this

    Goes to


    Wait. Is that even the answer? I'm confused.
    Earboth has outlined the method - your task is to multiply \frac{1}{8 \cdot 2\sqrt{2}} by  \frac{\sqrt2}{\sqrt2}<br />
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  9. #9
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    Here's a more obvious way...

    \frac{1}{8\sqrt{8}}=\frac{\sqrt{2}}{\sqrt{2}}\ \frac{1}{8\sqrt{8}}=\frac{\sqrt{2}}{8\sqrt{2}\sqrt  {8}}

    =\frac{\sqrt{2}}{8\sqrt{2(8)}}=\frac{\sqrt{2}}{8\s  qrt{16}}

    =\frac{\sqrt{2}}{8(4)}=\frac{\sqrt{2}}{32}
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  10. #10
    Senior Member Mukilab's Avatar
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    Edit: I saw Mr Meade's post. Thank you very much
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  11. #11
    Super Member bigwave's Avatar
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    Quote Originally Posted by Mukilab View Post
    Method and WIP please ^^

    \frac{1}{8\sqrt{8}}

    Give answer in the form \frac{\sqrt{2}}{p} Where p is a positive interger
    here is another way to look at it

    \frac{1}{8\sqrt{8}} \times \frac{\sqrt{8}}{\sqrt{8}}<br />
\Rightarrow<br />
\frac{\sqrt{8}}{8*8}<br />
\Rightarrow<br />
\frac{\sqrt{2}\sqrt{4}}{64}<br />
\Rightarrow<br />
\frac{2\sqrt{2}}{64}<br />
\Rightarrow<br />
\frac{\sqrt{2}}{32}<br />
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  12. #12
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by bigwave View Post
    here is another way to look at it

    \frac{1}{8\sqrt{8}} \times \frac{\sqrt{8}}{\sqrt{8}}<br />
\Rightarrow<br />
\frac{\sqrt{8}}{8*8}<br />
\Rightarrow<br />
\frac{\sqrt{2}\sqrt{4}}{64}<br />
\Rightarrow<br />
\frac{2\sqrt{2}}{64}<br />
\Rightarrow<br />
\frac{\sqrt{2}}{32}<br />
    Even better, thanks
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  13. #13
    MHF Contributor
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    Or...

    \frac{1}{8\sqrt{8}}=\frac{\sqrt{2}}{p}

    p(1)=8\sqrt{2}\sqrt{8}
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  14. #14
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    Quote Originally Posted by e^(i*pi) View Post
    you need to know that \sqrt{a^2} = a

    Precisely \sqrt{a^2} = |a|
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  15. #15
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    No, that's only one of them.
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