In this study, we aimed to find problematic and supportive issues in Afghan undergraduate students' proofs of the irrationality of [square root]3 and [square root]5/8 while using the indirect proof method. Collecting and analyzing produced proofs of 30 sophomore and 48 senior undergraduate students on the irrationality of [square root]3 and [square root]5/8, respectively, revealed that the majority were not able to extend indirect proof beyond showing the irrationality of [square root]2 due to not being able to apply the supportive 'multiples of an integer' notion in their reasoning process of the irrationality of [square root]3, and this notion was not supportive in the case of showing irrationality of [square root]5/8, and finally we propose the method of finding nonzero integral solutions to the resulted Diophantine equation and using the rational roots theorem to prove that [square root]p/q is irrational.