An irrational number.
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No. In fact the sum of a rational and an irrational MUST be irrational.
The value of the sum depends on the values of the rational number and the irrational number.
It is always irrational.
The sum is irrational.
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.