EDB — 200

[200] Let’s fix an integer $N\ge 2$ that it is not a perfect square. Consider the subset $F$ of $ℝ$ given by the numbers $x$ that can be written as $x=a+b\sqrt{N}$, with $a,b\in \mathbb{Q}$; we associate the operations of $ℝ$: show that $F$ is a field.