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To say a set is closed under multiplication means that if you multiply any two numbers in the set, the result is always a member of the set.

If, say, the 2 numbers are radical 2 and radical 2 we have (1.4142...)(1.4142...) which by definition equals 2. The result is not an irrational number, so the set is not closed.

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Q: Are irrational numbers closed under multiplication?
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