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Irrational Proof

I have a question. I realize that two rational numbers added together equal a rational number and that a rational added to a irrational equal a irrational number; but how do I show what a irrational plus a irrational equal?
 

StatusX

Homework Helper
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They can be either. For example, Sqrt(2) + (2 - Sqrt(2)) is rational but Sqrt(2) + Sqrt(3) is not.
 
Do I just do two separate cases then?
 

StatusX

Homework Helper
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For what? There's nothing to prove.
 
So is it ok for me to just say that then? With no steps of the proof?
 

dextercioby

Science Advisor
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You can say:"When adding two irrational numbers,there's no rule/theorem to tell us the algebric nature of the resulting number"...

Daniel.
 

Hurkyl

Staff Emeritus
Science Advisor
Gold Member
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First, you need to figure out what you're trying to say. Then, worry about how to justify it.
 

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