Problem #PRU-98299

Problem

a) Could an additional $6$ digits be added to any $6$-digit number starting with a $5$, so that the $12$-digit number obtained is a complete square?

b) The same question but for a number starting with a $1$.

c) Find for each $n$ the smallest $k=k(n)$ such that to each $n$-digit number you can assign $k$ more digits so that the resulting $(n+k)$-digit number is a complete square.