Is product of a rational number and an irrational number, a rational number? Is product of two irrational numbers a rational number or irrational number? Justify giving examples.
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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 = √2
=> 0 x √2 = 0, which is a rational number.
ii. rational number = 2
irrational number = √2
=> 2 x √2 = 2√2 , which is an irrational number.
The product of two irrational numbers can be a rational number or an irrational number.
Examples:
i. √2 x √2 = √4 = 2, which is a rational number
ii. √2 x √3 = √6 , which is an irrational number
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