16974441796

1 = 1^2

16 = 4^2

169 = 13^2

169744 = 412^2

16974441796 = 130286^2

1,4 or 9 would satisfy the first part

16 or 49 would satisfy the next part

169 is the only number that satisfies the next part

To proceed we need a square number that lies between 169000 and 169999. By taking the square root of both those numbers, we find the only whole number between them is 412, therefore 412^2 = 169744 is the only number which satisfies the next part.

Similarly, we take the square root of 16974400000 and 16974499999 and find only one whole number between them: 130286. Therefore the answer is 130286^2 = 16974441796.