The aim of this study is to examine the 8th grade students' knowledge formation processes on square root numbers. The case study model, one of the qualitative research methods, was used as the research design, since it was aimed to examine how the knowledge creation processes of students with different mathematical achievements were formed in the research. The participants of the research are nine eighth grade students. Pilot application was carried out with three students and the main application was carried out with six students. Four practice questions were created in order to examine the eighth grade students' processes of forming the concept of square root numbers. The data collection tools of the research are the video recordings recorded during the semi-structured interview while the students answer the questions and the researcher notes obtained by the participant observation technique. The data of the research were analyzed using the descriptive analysis method. According to the findings of the study, a total of two students, one student in the pilot application and one student in the main application, reached the construction stage, out of nine students who participated in the research for the concept of irrational number. While students with moderate mathematics achievement reached the recognizing and building steps, some of the students with low mathematics achievement could not reach the recognizing or building steps.