2 and 288
24 24 times
24 x 24 = 576
The square numbers integers between 576 and 10000 (and their square roots, in the left column) are: 245762562526676277292878429841309003196132102433108934115635122536129637136938144439152140160041168142176443184944193645202546211647220948230449240150250051260152270453280954291655302556313657324958336459348160360061372162384463396964409665422566435667448968462469476170490071504172518473532974547675562576577677592978608479624180640081656182672483688984705685722586739687756988774489792190810091828192846493864994883695902596921697940998960499980110010000
624
There are infinitely many possible answers. An easy pair is 1 and 576
Three of them.
576, 4356, 6400 are perfect squares.
288 x 2
576 & 625
288, 576, 864 and 1152
624