Rational dependence

In mathematics, a collection of real numbers is rationally independent if none of them can be written as a linear combination of the other numbers in the collection with rational coefficients. A collection of numbers which is not rationally independent is called rationally dependent. For instance we have the following example.

${\displaystyle {\begin{matrix}{\mbox{independent}}\qquad \\\underbrace {\overbrace {3,\quad {\sqrt {8}}\quad } ,1+{\sqrt {2}}} \\{\mbox{dependent}}\\\end{matrix}}}$

Because if we let ${\displaystyle x=3,y={\sqrt {8}}}$, then ${\displaystyle 1+{\sqrt {2}}={\frac {1}{3}}x+{\frac {1}{2}}y}$.