[200] Let’s fix an integer \(N≥ 2\) 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 \(a,b∈ℚ\); we associate the operations of \(ℝ\): show that \(F\) is a field.
