Once Rahul's class had gone to a math museum for a picnic. However, Rahul decided to venture out on his own and explore the different exhibits. He didnt realise that he had entered the puzzle room. When he reached the end of the room, he realised that in order to proceed to the next room he has to solve a puzzle.
There were 15 blocks placed before him numbered from 1 to 15. He had to place them linearly in such a way that the sum of the numbers written on any two adjacent blocks is always a perfect square. Here's how the blocks were arranged when he entered the room:
              
How will he do it? Provide a detailed explanation along with your answer.