Question

Which number produces an irrational number when multiplied by 1/2

Answer 1

Quick answer

Any irrational number. I can't think of any exception to this statement.

sqrt(5) is irrational.  1/2 * sqrt(5) is still irrational.

-sqrt(5) is irrational. -1/2 * sqrt(5) is still irrational

2 + sqrt(5) is irrational. Multiplying this by 1/2 is still irrational.

1/2(2 + sqrt(5) = 1 + 1/2 * sqrt(5) ) is irrational.

Conclusion

There are no exceptions to this.  All irrational numbers produce irrationals when multiplied by 1/2