Test takers should know 20^2 = 400, and 25^2 = 625. Since 479 is closer to 400 than to 625, we might guess the answer will be A or B here, and test out 22^2 to see where we are.
22^2 = (20 + 2)(22) = 440 + 44 = 484
and since 479 is just less than 22^2, we can be sure √479 will be between 21 and 22, and the answer is A.
I'd add: knowing the squares between 20^2 and 25^2 would be slightly useful in this particular question, but the probability that knowledge would help on a given GMAT test is nearly zero, so if a prep book suggests memorizing squares that large, my advice would be to ignore the recommendation.
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