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yes..always a perfect square

A perfect square is the product of an integer by itself. If you multiply a perfect square

x² by another perfect square y² you get x²y² = x·x·y·y = x·y·x·y = (x·y)² which is a perfect square.

Note that the product of two integers will also be an integer so x·y must be an integer because if x² and y² are perfect squares x must be an integer and y must be an integer and x·y is therefore a product of 2 integers.

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Q: Is the product of two perfect squares sometimes a perfect square?
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