Writing a proof the correct way

[grjmmr]

Homework Statement

k:= {s+t√2:s,t\inQ}, if x1 and x2 \in K, prove x1 +x2\inK

Homework Equations

The Attempt at a Solution

My thought is that x1 and x2 \inK\inQ\subseteqR thus by algerbraic properties X1+x2 =X3 which also \in K. this seems just a little too easy, am i correct in my line of thinking?

 

[LCKurtz]

Homework Statement

k:= {s+t√2:s,t\inQ}, if x1 and x2 \in K, prove x1 +x2\inK

Homework Equations

The Attempt at a Solution

My thought is that x1 and x2 \inK\inQ\subseteqR thus by algerbraic properties X1+x2 =X3 which also \in K. this seems just a little too easy, am i correct in my line of thinking?

You need more detail. What you have to show is that $x_1+x_2$ can be written in the form $s+t\sqrt 2$ where $s,t\in Q$, where I presume $Q$ is the rationals, although you never specifically said that.