Jimmy!

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

WOOOOOW

but that isn't in simplest form.

hmm not working, ok one sec

Thanks.

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...

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

Join our real-time social learning platform and learn together with your friends!