I need to rationalize: 9 cuberoot of 2 over cuderooot of 5 - cuberoot of 2

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- Jul 15th 2009, 02:22 PMkandela573how do i start
I need to rationalize: 9 cuberoot of 2 over cuderooot of 5 - cuberoot of 2

- Jul 15th 2009, 02:29 PMPlato
Recall that $\displaystyle (a^3 -b^3)=(a-b)(a^2+ab+b^2)$.

$\displaystyle \frac{{\sqrt[3]{9}}}{{\sqrt[3]{5} - \sqrt[3]{2}}}\left( {\frac{{\sqrt[3]{{25}} + \sqrt[3]{{10}} + \sqrt[3]{4}}}{{\sqrt[3]{{25}} + \sqrt[3]{{10}} + \sqrt[3]{4}}}} \right)=?$ - Jul 15th 2009, 02:38 PMkandela573
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?(Thinking)

- Jul 15th 2009, 02:59 PMVonNemo19
- Jul 15th 2009, 03:41 PMPlato