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Math Help - Rationalizing the Denominator #2

  1. #1
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    Rationalizing the Denominator #2

    i have 2 more question that i tried to do but not sure do i have to go further. Thanks.

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    Quote Originally Posted by xJenniferx View Post
    i have 2 more question that i tried to do but not sure do i have to go further. Thanks.

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    For the first one, you forgot \sqrt{a-b} in the numerator again !

    \frac{\sqrt{a-b}\sqrt{a+b}}{a-b}=\frac{\sqrt{(a-b)(a+b)}}{a-b}=\frac{\sqrt{a^2-b^2}}{a-b}

    For the second one, assume that x,y>0 :

    \frac{\sqrt{x^3 y^5}}{x^3y^5}=\frac{\sqrt{x^2 y^4 xy}}{x^3y^5}=\frac{xy^2 \sqrt{xy}}{x^3y^5}=\dots
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    Rationalizing the Denominator means taking the square root away....
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    Quote Originally Posted by xJenniferx View Post
    i have 2 more question that i tried to do but not sure do i have to go further. Thanks.

    Link to problem.
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      \frac{{\sqrt {a + b} }}<br />
{{\sqrt {a - b} }} \hfill \\

      = \frac{{\sqrt {a + b} }}<br />
{{\sqrt {a - b} }} \times \frac{{\sqrt {a - b} }}<br />
{{\sqrt {a - b} }} \hfill \\

       = \frac{{\sqrt {\left( {a + b} \right)\left( {a - b} \right)} }}<br />
{{a - b}} \hfill \\

      = \frac{{\sqrt {a^2  - b^2 } }}<br />
{{a - b}} \hfill \\<br />
   \hfill \\

     {\text{Now, for second question}}{\text{.}} \hfill \\

      \frac{1}<br />
{{\sqrt {x^3 y^5 } }} = \frac{1}<br />
{{\sqrt {x^2 xy^4 y} }} = \frac{1}<br />
{{xy^2 \sqrt {xy} }} \hfill \\

       = \frac{1}<br />
{{xy^2 \sqrt {xy} }} \times \frac{{\sqrt {xy} }}<br />
{{\sqrt {xy} }} \hfill \\

      = \frac{{\sqrt {xy} }}<br />
{{xy^2 xy}} = \frac{{\sqrt {xy} }}<br />
{{x^2 y^3 }} \hfill \\ <br />
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    Quote Originally Posted by xJenniferx View Post
    Rationalizing the Denominator means taking the square root away....
    Yes, but if you want to do so, you're likely to have square roots in the numerator. You can't just "forget" them !
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