Can ALU do square roots?
No - computing a square root with any degree of accuracy is both
a numerical and iterative process. Because of this, it can not be
calculated with a combinatorial circuit like an ALU. It requires a
sequential circuit, so you at the very least need some memory
paired with the ALU to compute a square root.
If you are interested in the numerical methods for calculating
square roots, go see the wikipedia page on the topic (check the
link).