Solution:
The product of a rational number and an irrational number can be a rational number
or an irrational number.
Examples:
i. rational number \(=0\)
irrational number \(=\sqrt{2}\)
\(=>0 x \sqrt{2}=0\), which is a rational number.
ii. rational number \(=2\)
irrational number \(=\sqrt{2}\)
\(=>2 x \sqrt{2}=2 \sqrt{2}\), which is an irrational number.
The product of two irrational numbers can be a rational number or an irrational
number.
Examples:
i. \(\sqrt{2} \times \sqrt{2}=\sqrt{4}=2\), which is a rational number
ii. \(\sqrt{2} \times \sqrt{3}=\sqrt{6}\), which is an irrational number
