1) Because for a given number (don't remember which one I used) using a random number generator to produce the proper value will yield 50 completely different results, one of which is the actual square root.
Still not sure where you're getting 50 from.
Even assuming he meant an honest random generator, and not just an arbitrary method, his method would always come up with the right answer. Even though using a random number would increase overhead, the method would still work. The part that drives it to be correct is the iterations of checking run, not how the number is acquired. And some simple calculators do just that.
MY point is that trial-and-error is a meaningless process if you don't have a parameter to define the CORRECT value in a reasonable amount of time
There is a parameter, and the time it takes isn't unreasonable. At least in regards to basic square root calculation. This analogy might not be the best fit to AI.