Apply a function in a criterion in Excel

Suppose I have in the column A a list of integers and I want to summarize them in B1. Then I can simply write =SUM(A:A). Suppose I want the sum of integers less than 10, so I can write SUMIF(A:A,"<=10"). What if now I want to add the integers that are perfect squares?

I could always make a column C with in the first cell (C1) =INT(SQRT(A1))=SQRT(A1), then =INT(SQRT(A2))=SQRT(A2) and so. Then I can probably write B1, Something like SUMIF(C:C,"TRUE",A:A), and then proceed to hide the ugly column C.

But is there no simpler and more orderly way of doing this? I can't seem to find a way to apply a function in a criterion. If for example @x they were a placeholder name (a variable) for the value in which the criterion is applied, you could write "@x<=10" for "<=10"but more usefully, I could write "INT(SQRT(@x))=SQRT(@x)" directly instead of making a C column as before. My question is then

Is there a simple way to create such useful criteria?