Who first described the technique of removing radicals as indicated in the answers to questions Tools for Removing Radicals from Equations and Rewrite sum of radicals equation as polynomial equation ?

When has it been described the first time and, what was the motivation? Was it actually an equation that involved square roots etc., or, has it been described as a proof, that equations involving radicals can be converted to polynomial equations?

I have already done a lot of online research without success; therefore I hope for answers from the MO community, even if the answers may be wellknown to experts in the field.