Ex) 나는 밥을 먹/으러 식당에 가요. I go to restaurant to eat. 나는 머리를 깍/으러 미장원에 가요. I go to hair shop to cut. 나는 손을 씻/으러 화장실에 가요. I go to bathroom to wash my hand . etc. 1. verb 먹다(eat), 깍다(cut), 씻다(wash) etc. If verb have final consonant can use " 으러" (먹)+으러= 먹으러, (깍)+ 으러=깍으러, (씻)+으러= 씻으러 etc. 2. verb 하다 (do) 보다(see) 사다(buy) ect . If verb have not final connant can uae " 러 " (하)+러= 하러, (보)+ 러= 보러, (사)+ 러 = 사러 etc. Ex) 나는 공부하/러 학교에 가요. (I go to school to study) 나는 영화보/러 영화관에 가요. ( I go to cinema to see a movie) 나는 옷 사/러 백화점에 가요. ( I go to department store to buy clothes) when verb expression a purpose can use " 러" " 으러"

The meaning is same but you should think separately for usuage. If there is final consonant in the verb you're going to use, you should use "으러". For example, 앉으러,(앉다sit, final consonat here is ㄵ), 잡으러(잡다catch), 놓으러(놓다put), 먹으러(먹다eat) With no final consonant, you can use ""러" like this. 공부하러(공부(noun)+하다=study), 불끄러(불끄다turn off the light)

Thanks for your help ^^ i understand better, now.

yes you are right. "으러" and '러" are the same meanning. those mean "for the purpose of" , "in order to" and the example is great. im going to library to stuy 나는 도서관에 공부하러 간다.