This is the first of two lessons in which students look closely at whether a solution to a quadratic equation is rational or irrational. Distinguishing solutions as rational or irrational does not necessarily impact students’ ability to solve applied problems about quadratic functions. In those cases, we deal mostly with finite decimal approximations. The work here extends students’ understanding of the real number system. Reasoning about the properties of rational and irrational numbers also offers opportunities to construct logical arguments and attend to precision in reasoning (MP3, MP6). Along the way, students also practice solving quadratic equations and finding zeros of the corresponding functions.