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Rational and Irrational Numbers — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSRational and Irrational Numbers1 Mark
Question
Write a pair of irrational numbers whose product is irrational.
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Answer

Consider two irrational numbers $( 5 + \sqrt2 )$ and $( \sqrt5 - 2 )$
Thus, the product,$ ( 5 + \sqrt2 ) \times ( \sqrt5 - 2 )$$= 5\sqrt5 - 10 + \sqrt10 - 2\sqrt2$ is irrational.

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