Question

What is the set of numbers to which `-sqrt22` belong?

Answer 1

The `-sqrt22` is equal to `-sqrt22=-sqrt(2*11)=-(sqrt2*sqrt11)`

Hence `sqrt2` , `sqrt11` are irrationals , `-sqrt22` is irrational.

When a number like `sqrta` can simplify to the form `p/q` where `p,q` where are natural number then it is called rational.

For example `-sqrt9=-sqrt(3^2)=-3`

Of course irrational numbers belong to the set of real numbers like the rationals , integers and natural numbers.