If squaring a number means multiplying that number with itself then shouldn’t taking square root of a number mean to divide a number by itself?
For example the square of 2 is 22=2⋅2=4 .
But square root of 2 is not 22=1 .
taking square root means reversing the effect of
squaring. Dividing a number by itself does not do that (but rather always returns 1 as you noted).
Compare your question to: if doubling a number means adding it to itself, shouldn’t halving a number mean subtracting it from itself? Answer: obviously not.