Kindly refer to the topic 1.6 'Some useful results on Irrational numbers' ( Page 1.26 RD Sharma) Kindly clarify the following points:-
a:- Theorem 4 (II) says that, ' The difference of the irrational numbers √2 and -√2 is 0, which is a rational number. Whereas, in my opinion √2 - (-√2)=√2+√2.
b: - Are all the irrational numbers added, subtracted, multiplied and divided in the same manner as other integers. For example, am I right if I say the following:-
iv. √6 / √3=√2
We have not understood the query that you have posted. We would request you to clarify / provide additional details so that we may answer this to the best of the ability.