Question
Write a pair of irrational numbers whose difference is irrational.
✓
Answer
$(\sqrt{3}+2)$ and $(\sqrt{2}-3)$ are irrational numbers whose difference is irrational.
Thus, we have
$(\sqrt{3}+2)-(\sqrt{2}-3)$
$=\sqrt{3}+2-\sqrt{2}+3$
$=\sqrt{3}-\sqrt{2}+5,$
which is irrational.
Thus, we have
$(\sqrt{3}+2)-(\sqrt{2}-3)$
$=\sqrt{3}+2-\sqrt{2}+3$
$=\sqrt{3}-\sqrt{2}+5,$
which is irrational.
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