Square Numbers Sudoku (Fun With Sudoku #35)

This Square Numbers Sudoku, I created for the 21st Indian Sudoku Mock Test. This is a very old Sudoku that was in my notebook without getting published. After many years I am publishing this Sudoku on this blog.
Sudoku Grand Prix Championship 2015 is going to start early next year with the instruction booklet of the first round already published. It contains many interesting Sudoku variations with two Sudoku variations Round Off Sudoku and Mathrax Sudoku being the new variations. I will be creating some of these unknown variations which are appearing in this championship soon and will publish these puzzles under The League of Extraordinary Ladies and Gentlemen. Do keep watch on this blog for these new variations.
This Square Numbers Sudoku I am posting as the 35th Sudoku in the Fun With Sudoku Series. Can you solve this Square Numbers Sudoku puzzle?

Rules of Square Numbers Sudoku

Classic Sudoku Rules apply. Additionally, greyed squares can only contain square numbers i.e. the number which we can get after doing the square of a number. In other words, greyed cells can contain only 1, or 4,9 numbers.