I know you're looking for long division but, to me, that doesn't seem like the fastest way to find you're answer.
Consider 5x5=25 and 6x6=36 so you're looking for something between 5 and 6.
5.5x5.5= 30.25
5.7x5.7=32.49
Soo... at this point you're close.
5.73x5.73=32.83
And finally
5.75x5.75=33.06
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Not sure you could find the square root with only division because a square like that isn't really obvious like 2x2 is to 4. If you divide 33/2, you get 16.5 but how do you known when to stop picking numbers to divide 33 with? Just a consideration.