No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving Irrational Numbers give you an irrational number, but there are a few exceptions.
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Such a sum is always rational.
Yes
Can be rational or irrational.
No. Two irrational numbers can be added to be rational. For example, 1/3 + 2/3 = 3/3. 1/3 and 2/3 are both irrational, but 3/3 = 1, which is rational.
The product of two rational numbers, as in this example, is always RATIONAL.However, if you mean 10 x pi, pi is irrational; the product of a rational and an irrational number is ALWAYS IRRATIONAL, except for the special case in which the rational number is zero.