Question

The sum or difference of a rational and an irrational number is___ ,

Answer 1

A rational number is defined as a number that can be written in $\frac{p}{q}$ form where $q\ne 0$ and $p,q$ are integers. The decimal expansion of these numbers either repeats or terminates at some point.

An irrational number’s decimal expansion will keep ongoing. It will never stop or repeat.

If one does addition or subtraction of rational and irrational numbers then the result will always be an irrational number because, after the addition or subtraction, numbers after decimal will never stop.

Hence, the blank will be filled by irrational.