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Mathematics
OpenStudy (saifoo.khan):

Jimmy!

OpenStudy (saifoo.khan):

jimthompson5910 (jim_thompson5910):

\[\large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})\] \[\large (\sqrt[5]{4})(\sqrt[5]{125})+(\sqrt[5]{4})(\sqrt[5]{8})+(-\sqrt[5]{2})(\sqrt[5]{125})+(-\sqrt[5]{2})(\sqrt[5]{8})\] \[\large \sqrt[5]{4*125}+\sqrt[5]{4*8}-\sqrt[5]{2*125}-\sqrt[5]{2*8}\] \[\large \sqrt[5]{500}+\sqrt[5]{32}-\sqrt[5]{250}-\sqrt[5]{16}\] \[\large \sqrt[5]{500}+2-\sqrt[5]{250}-\sqrt[5]{16}\] \[\large 2+\sqrt[5]{500}-\sqrt[5]{250}-\sqrt[5]{16}\] So \[\large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})=2+\sqrt[5]{500}-\sqrt[5]{250}-\sqrt[5]{16}\]

OpenStudy (saifoo.khan):

WOOOOOW

OpenStudy (saifoo.khan):

but that isn't in simplest form.

jimthompson5910 (jim_thompson5910):

hmm not working, ok one sec

OpenStudy (saifoo.khan):

Thanks.

jimthompson5910 (jim_thompson5910):

well none of the other terms simplify, but you could combine the second pair of terms to get \[\large (\sqrt[5]{2}-1)\sqrt[5]{250}\], but that's not much of a simplification...

jimthompson5910 (jim_thompson5910):

So \[\large \large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})=2+(\sqrt[5]{2}-1)\sqrt[5]{250}-\sqrt[5]{16} \]

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