I need to find a subring of $\mathbb{ R }$ isomorphic to $\mathbb{ Q }[ x ] / \langle x^3 - 2 \rangle$.
I considered using the Isomorphism Theorem to try to find a homomorphism $\theta: \mathbb{ Q }[x] \to R \subseteq \mathbb{ R }$ such that $\langle x^3 - 2 \rangle = \ker \theta$, so then $R \cong \mathbb{ Q }[ x ] / \langle x^3 - 2 \rangle$. But I was unsure of where to proceed.