which subset of real numbers does it belong to

The [tex]\sqrt{30}[/tex] would be considered an irrational number, or the third answer choice. This is because you cannot easily write [tex]\sqrt{30}[/tex] as a fraction, or ratio, hence the name "irrational."
This is unlike a number like 1.5, which you can create a fraction based on: [tex]\frac{3}{2}[/tex].