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## Homework Statement

k:= {s+t√2:s,t[itex]\in[/itex]

**Q**}, if x1 and x2 [itex]\in[/itex] K, prove x1 +x2[itex]\in[/itex]K

## Homework Equations

## The Attempt at a Solution

My thought is that x1 and x2 [itex]\in[/itex]K[itex]\in[/itex]

**Q**[itex]\subseteq[/itex]

**R**thus by algerbraic properties X1+x2 =X3 which also [itex]\in[/itex] K. this seems just a little too easy, am i correct in my line of thinking?