The correct option is D The product and quotient of a non-zero rational and irrational number is irrational.
Option A does not always hold true as √2×√2=2, which is rational.
Sum of two irrational number can also be rational. Here is one example among many possibilities: (5−√2)+(4−√2)+2√2=9. Thus option B does not always hold true.
For different rational and irrational values, statement in option C failed to hold. But option D is true always.