General :: Case Statements In Bash Scripts

while learning to write bash scripts, i decided to write some script that, given an integer as input, will tell you the square root of that integer (provided the integer in question is a perfect square). i have already done on using primarily if statements and a while loop. i decided that using a case statement would be a lot simpler and i would be able to make the script more functional. here is what i have so far

[Code]....

i have tried all posible combos of using -ge or >= but i get pretty much the same thing.
the idea is, for now, if the input is greater than or equal to 0 that it will echo test. can you do this sort of thing with case statements? or will it only work if i give it specific values like [1-9] (if this is the case then i dont think the case statement will work for what i want to do)