Let K := {s + t2 : s; t Q}. Show that K satisfies the following:

Question:

Let K := {s + t√2 : s; t ∈ Q}. Show that K satisfies the following:
(a) If x1; x2 ∈ K, then x1 + x2 ∈ K and x1x2 ∈ K.
(b) If x ≠ 0 and x ∈ K, then 1/x ∈ K.
(Thus the set K is a subfield of R. With the order inherited from R, the set K is an ordered field that lies between Q and R.)