Question

Jimmy!

Answer 1

\[\large (\sqrt[5]{4}-\sqrt[5]{2})(\sqrt[5]{125}+\sqrt[5]{8})\]



\[\large (\sqrt[5]{4})(\sqrt[5]{125})+(\sqrt[5]{4})(\sqrt[5]{8})+(-\sqrt[5]{2})(\sqrt[5]{125})+(-\sqrt[5]{2})(\sqrt[5]{8})\]



\[\large \sqrt[5]{4*125}+\sqrt[5]{4*8}-\sqrt[5]{2*125}-\sqrt[5]{2*8}\]



\[\large \sqrt[5]{500}+\sqrt[5]{32}-\sqrt[5]{250}-\sqrt[5]{16}\]



\[\large \sqrt[5]{500}+2-\sqrt[5]{250}-\sqrt[5]{16}\]



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

Answer 2

WOOOOOW

Answer 3

but that isn't in simplest form.

Answer 4

hmm not working, ok one sec

Answer 5

Thanks.

Answer 6

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...

Answer 7

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