# Writing a proof the correct way

## Homework Statement

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

## The Attempt at a Solution

My thought is that x1 and x2 $\in$K$\in$Q$\subseteq$R 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 Helper
Gold Member

## Homework Statement

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

## The Attempt at a Solution

My thought is that x1 and x2 $\in$K$\in$Q$\subseteq$R 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.