Question
Write a pair of irrational numbers whose product is rational.
✓
Answer
$(\sqrt{3}+\sqrt{2})$ and $(\sqrt{3}-\sqrt{2})$ are irrational numbers whose product is rational.
Thus, we have
$(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})$
$=(\sqrt{3})^2-(\sqrt{2})^2$
$=3-2$
$=1$, which is a rational number.
Thus, we have
$(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})$
$=(\sqrt{3})^2-(\sqrt{2})^2$
$=3-2$
$=1$, which is a rational number.
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