They are: 529 and 576
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Well, honey, the perfect squares between 500 and 600 are 529 (23^2) and 576 (24^2). Hope that clears things up for ya!
The halfway point between 500 and 600 is (500 + 600) ÷ 2 = 550
500
550 is halfway between 500 and 600
496
100