Question

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

Answer 1

Answer:

Nope it isn't necessary.

Justification:

One example is enough to prove this wrong so,

Let  $\\\tt x = \sqrt{2}$ and $\\\tt y = \sqrt{8}$

Now,

$\\\tt xy = \sqrt{2 \times 8} \\ = \sqrt{16} \\ = +4 \: or \: -4$