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Kruka [31]
3 years ago
11

Rationalize the numerator.

rt%5B3%5D%7By%7D%20%7D%20" id="TexFormula1" title=" \frac{ \sqrt[3]{144x } }{ \sqrt[3]{y} } " alt=" \frac{ \sqrt[3]{144x } }{ \sqrt[3]{y} } " align="absmiddle" class="latex-formula">
Mathematics
2 answers:
Simora [160]3 years ago
3 0

rationalizing the numerator, or namely, "getting rid of that pesky radical at the top".


we simply multiply top and bottom by a value that will take out the radicand in the numerator.


\bf \cfrac{\sqrt[3]{144x}}{\sqrt[3]{y}}~~
\begin{cases}
144=2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\\
\qquad 2^3\cdot 18
\end{cases}\implies \cfrac{\sqrt[3]{2^3\cdot  18x}}{\sqrt[3]{y}}\implies \cfrac{2\sqrt[3]{  18x}}{\sqrt[3]{y}}
\\\\\\
\cfrac{2\sqrt[3]{  18x}}{\sqrt[3]{y}}\cdot \cfrac{\sqrt[3]{(18x)^2}}{\sqrt[3]{(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)(18x)^2}}{\sqrt[3]{(y)(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)^3}}{\sqrt[3]{18^2x^2y}}


\bf \cfrac{2(18x)}{\sqrt[3]{324x^2y}}~~
\begin{cases}
324=2\cdot 2\cdot 3\cdot 3\cdot 3\cdot 3\\
\qquad 12\cdot 3^3
\end{cases}\implies \cfrac{36x}{\sqrt[3]{12\cdot 3^3x^2y}}
\\\\\\
\cfrac{36x}{3\sqrt[3]{12x^2y}}\implies \cfrac{12x}{\sqrt[3]{12x^2y}}

Kipish [7]3 years ago
3 0

 ∛144x

-----------

   ∛y


   ∛8 ∛18x           ∛y^2

= -------------- * ----------------

    ∛y                    ∛y^2


    2 ∛18xy^2

= ------------------

          ∛y^3


     2 ∛18xy^2

= ------------------

           y

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