Statement: The sum of two irrational numbers may be rational or irrational.
Like the product of two irrational numbers, the sum of two irrational numbers will also result in a rational or irrational number.
For example, if we add two irrational numbers, say 3√2+ 4√3, a sum is an irrational number.
But, let us consider another example, (3+4√2) + (-4√2 ), the sum is 3, which is a rational number.
So, we should be very careful while adding and multiplying two irrational numbers, because it might result in an irrational number or a rational number.
> If two irrational numbers have no rational cofactors
What's this supposed to mean? I was unable to document the existence of any term "cofactor" that might apply to irrational numbers.
All pairs of irrational numbers share rational factors, to the extent that it makes sense to talk about factors of non-integral numbers, which it doesn't.
