- #1
Seydlitz
- 263
- 4
The methods of proving irrational have always been bothering me in my study of proof. It seems that for each case a new method has to be invented out of the blue. I understand only the proof that ##\sqrt{k}## is irrational. But what will happen if I want to prove ##\sqrt{2}+\sqrt{5}## or ##\sqrt{6}-\sqrt{5}##? Is it enough just to show each of them is irrational? Clearly it's not enough considering ##\sqrt{2} - \sqrt{2}## is rational. Could you guys help me in giving hint on how to prove them? It just doesn't seem obvious for me, at least for now. Most of the textbooks that I have read simply assume that once they have shown that square root of 2 is irrational, then the method can be applied to other form of irrationals.
Thank You
Thank You