Perfectly Squared Dice

Two strange six-sided dice are numbered on each side as follows:

  • Die A: 2, 2, 3, 3, 4, 4
  • Die B: 1, 2, 3, 4, 8, 12

If one were to roll these dice at the same time and multiply the two resulting values, what is the probability that the product would be a perfect square?

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