[tex]\begin{gathered} \sqrt[]{18\text{ }}can\text{ be simplified further as } \\ \sqrt[]{2}\times\sqrt[]{9} \\ 3\sqrt[]{2} \\ \text{Therefore the subsets of the number system in which 3}\sqrt[]{2}\text{ belongs are} \\ \text{irrational numbers and counting numbers} \end{gathered}[/tex]
The subsets are {irrational numbers, counting numbers}
The number shown is not a rational number, not a whole number and not an integer.