Which subsets of the real numbers does the number spaure root of 42 belong to

Ok

so we first got natural number or counting numbers
this is like 1,2,3,4 etc

then whole numbers, that is natural numbers plus 0
so 0,1,2,3,4, etc

then integers, that is whole numbers plus negatives
so -4,-3,-2,-1,0,1,2,3,4 etc

then rational numbers, these are numbers that can be written in form a/b where a and b are integers and b≠0
so like -4/1 or 1/2 or something like that

then irrational numbers, these can't be written in a/b form, they have to have a symbol or an unsimplified square root
exmaples, π, √2

these are the sets that make up real numbers

note: an irrational number times a rational number results in an irrational number

so
√42=(√2)(√3)(√7)
√2 is irrational so √42 is irrational

it belongs to the irrational numbers subset