Compare the integer square root algorithm used in "Spacewar!" [1]. So, even by 1960 it should have been possible to implement a square root step instructions for each bit, much like division or multiplication shifts, and progress from this to full-fledged automatic operations by the use of a sub timing network. (I guess, it really depends on the economics of the individual use case, whether the effort does pay off or not, as you would amass a few additional hardware modules to accomplish this.)

[1] https://www.masswerk.at/spacewar/inside/insidespacewar-pt6-g...