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No. The product of conjugate pairs is always rational.

So suppose sqrt(y) is the irrational square root of the rational number y. Then

Thus [x + sqrt(y)]*[x - sqrt(y)] = x^2 + x*sqrt(y) - x*sqrt(y) - sqrt(y)*sqrt(y)

= x^2 + y^2 which is rational.

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Q: Are the products of irrational numbers always irrational?
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