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Question
Write a pair of irrational numbers whose product is irrational.
Solution
Consider two irrational numbers `(5 + sqrt(2)) and (sqrt(5) - 2)`.
Thus, we have
`(5 + sqrt(2)) (sqrt(5) - 2)`
= `5(sqrt(5) - 2) + sqrt(2)(sqrt(5) - 2)`
= `5sqrt(5) - 10 + sqrt(10) - 2sqrt(2)`, which is irrational.
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