400 can be factored as 24 * 52, or 22 * 22 * 52. A perfect square factor of 400 will always have an even exponent, so here is a list:
12, 22, 42, 52, 102, and 202.
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They are all perfect squares
496
20 squares x 20 squares = 400 squares
501
They are: 529 and 576