Is $\mathbb{Q}(\sqrt(2)\sqrt[3](5)) \subset \mathbb{Q}(\sqrt{2}+\sqrt[3]{5})$?
I've tried writing any element $x \in \mathbb{Q}(\sqrt(2)\sqrt[3](5)$ with $x = a + b\sqrt(2)\sqrt[3](5)$ in terms of $a + b(\sqrt{2}+\sqrt[3]{5})$, but I can't find a way. Anyone know how to approach this?