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.
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Such a sum is always rational.
Such a sum is always irrational.
Can be rational or irrational.
The square root of any positive integer can only be a WHOLE NUMBER or IRRATIONAL, so the square root of 7 is irrational.On the other hand, the sum of a rational and an irrational number is always irrational.
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.