Chapter 5.3, Problem 14E

Let $D$ be the set of all real numbers of the form $m+n\sqrt{2}$, where $m,n\in \mathbb{Z}$. Carry out the construction of the quotient field $Q$ for this integral domain, and show that this quotient filed is isomorphic to the set of real numbers of the form $a+b\sqrt{2}$ where $a$ and $b$ are rational numbers.