In some high school text books I find theorems called "Irrational Conjugate Theorem" (or similar) related to irrational roots of rational polynomials. More precisely they call the number $p-\sqrt{q}$ the "conjugate" of $p+\sqrt{q}$ ($p$, $q$ rationals, $\sqrt{q}$ not rational). The statements themselves are (more or less) correct, but I find it strange to use the phrase "conjugate" in this context.
I searched on the web and I did not find any resources above high school level that uses this term. I also searched on this forum and when a question asks about irrational conjugates (there are quite a few) the answers and comments mostly start along the lines "what do you mean by conjugate?"
My question is the following. Is there a universally accepted definition of a conjugate of irrational numbers (or certain type of irrational numbers)? If yes, I would appreciate a reference to a proper resource (not a high school text or a website helping high school students with their homework).