Question

Which number produces a rational number when multiplied by 1 over 3

Answer 1

Any irrational number will remain irrational when multiplied by a rational number.

For example:
π * 1/3 = π/3
√2 * 1/3 = (√2)/3

But if you multiply by a *rational* number, the result will stay rational.

Answer:
Any irrational number (e.g. π, √2, √3, etc.)