I need to rationalize: 9 cuberoot of 2 over cuderooot of 5 - cuberoot of 2
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Recall that $\displaystyle (a^3 -b^3)=(a-b)(a^2+ab+b^2)$. $\displaystyle \frac{{\sqrt[3]{9}}}{{\sqrt[3]{5} - \sqrt[3]{2}}}\left( {\frac{{\sqrt[3]{{25}} + \sqrt[3]{{10}} + \sqrt[3]{4}}}{{\sqrt[3]{{25}} + \sqrt[3]{{10}} + \sqrt[3]{4}}}} \right)=?$
okay but in order for it to be simplified i can't have a radicand in the denominator so do i mulitply everything by the third power?
Originally Posted by kandela573 okay but in order for it to be simplified i can't have a radicand in the denominator so do i mulitply everything by the third power? Follow through with the multiplication that Plato has indicated and see what happens.
Originally Posted by kandela573 okay but in order for it to be simplified i can't have a radicand in the denominator so do i mulitply everything by the third power? Can you do this, $\displaystyle \left( {\sqrt[3]{5} - \sqrt[3]{2}} \right)\left( {\sqrt[3]{{25}} + \sqrt[3]{{10}} + \sqrt[3]{4}} \right)=?$ If not, why were you asked to do this problem?
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