number theory - last digit is a square and.....

I've found some solutions for this questions but they were not impressive.

Question:

How many natural numbers are there in base $10$,whose last digit is perfect square,combination of last two digits is a perfect square,combination of last three digits is a perfect square,$\ldots$,combination of last $n$ digits is a perfect square?

For example $64$ is a number whose last digit is a perfect square and combination of last two digits is also a perfect square.

Kindly tell me how to approach this question.

Answer

Answers are in the forms:-

(i)$4\times10^n$

(ii)$9\times10^n$

(iii)$10^n$

(iv)$49\times10^n$

(v)$64\times10^n$

(vi)$81\times10^n$

Where $n \in 0,2,4,6...$