@Chris Page offered a perfectly acceptable answer, because it addresses all of your necessary issues, but then I took a second look at your code and wondered why not use a function with a loop instead of all those variable commands?
ink() {
square_dimension="$2"
infile="$1"
/Applications/Inkscape.app/Contents/Resources/bin/inkscape --export-png "${root}/test_${square_dimension}.png" -w ${square_dimension} -h ${square_dimension} "$infile"
}
for i in {256,128,64,48,40,32,24,16}; do ink "$1" "$i"; done
Note that the above code has not been tested, and it is not your complete script, just a snippet that will replace the majority of your code. I will update after I have had a chance to test it, but it looks good to me. You may need to export the function or something (export -f ink) or mess around with the argument variables -- but like I said, I will post an update after I've had a chance to test it.
Also, like I said before, @Chris Page offered an answer that pretty much answers your question. This is simply additional info that is better formatted as an answer rather than multiple comments.
Also, it's best practices to always use lowercase variable names in shell scripts so as not to overwrite any of the built-in environment variables (which is something that I have struggled with, because the variables are so much easier to recognize -- especially in a large script on a system without a colored terminal for syntax highlighting).