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

The $- \sqrt{22}$ is equal to $- \sqrt{22} = - \sqrt{2 \cdot 11} = - \left(\sqrt{2} \cdot \sqrt{11}\right)$
Hence $\sqrt{2}$ , $\sqrt{11}$ are irrationals , $- \sqrt{22}$ is irrational.
When a number like $\sqrt{a}$ can simplify to the form $\frac{p}{q}$ where $p , q$ where are natural number then it is called rational.
For example $- \sqrt{9} = - \sqrt{{3}^{2}} = - 3$