St1 says d is square of an integer. where you have considered d = 1*2, that is incorrect as 2 is not a square of any integer. root2 is not an integer.
if you consider D to be integer sqaures like 1,4,9,16,25 .... you will always find that rootD is an integer (1,2,3,4,5 ... ) for the above case

Hence 1 is sufficient also.

Id d is a positive integer, is √d an integer

1.d is a square of an integer
2.√d is the square of an integer

The correct answer is D

I understand how statement 2 is sufficient, But how is statement 1 sufficient

if d = 2^2 = 4 then √4 = integer
but
if d = 1^2 = 1 then √1 is not an integer

so statement 1 is not sufficient

We are given d is a positive integer and asked to find out if root d is an integer.
1)For your questions : root 1 is 1 which is an integer. Hence A is sufficient.