If a nine digit number is formed by the nine non zero digits with units digit $5$, prove that it must not be a perfect square.
Greetings, I was continuing on with my number theory, and a question came again which I could not solve.
Here's what I've done so far:
Since the units digit of the 9 digit number is $5$, it is a multiple of $5$. Therefore the number is divisible by $25$ and hence the last two digits are $25$ and now I'm stuck.
Any help would be appreciated.
Thank You
EDIT: Thanks to John Omielan, Toby Mak, Community♦ for pointing out that this is a duplicate. See the first link on the top. There is an answer there.