Question

Let x be rational and y be irrational . Is xy necessarily irrational ? Justify your answer by an example

Answer 1

Not necessarily. If I put x as 0 and take y as any irrational no., the product is 0 that is rational. If we take x as any other rational no., the product will be irrational.

Answer 2

$\bold{Hello \ friends}$

No, It's not necessary that xy is irrational.

For example:

x= 0 (Rational),

$y = \sqrt{2} \: irrational \\ xy = 0 \times \sqrt{2} \\ = 0 \: which \: is \: not \: irratinal$