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