In general, the approach of irrational numbers during school years in Basic Education is restricted to a few 

examples, the roots of numbers two and three (\ sqrt {2 \} and \ sqrt3 \) are usually presented, and the 

number pi (\ pi). In this project, we aim to carry out research on some other numbers represented in 

the form of radicals \ sqrt n, being n \ in N. We analyzed the productions made and discussed by 

students of a degree course in Mathematics at a Federal University of Baixada Fluminense . 

The methodological procedures of the research were: bibliographic survey for the elaboration, 

implementation and analysis of proposed activities. For data collection, the researcher's field diary, 

video and audio record of the meetings and the written record of the participants' responses were used. 

The analysis sought to identify how students classify the numbers presented, how they interpret and solve 

the tasks presented. In this way, we seek to understand the strategies used by the researched group in view 

of the different situations proposed and to elaborate, from this analysis, a didactic guide, for teachers 

with new suggestions of activities for the study of irrational numbers. 

The results show that students consider constant intervals between the numbers presented when they were

 asked to represent them on the real line, repeating the idea of ordering the naturals.