Question

Is the sum or product of two irrational numbers always irrational?

Answer 1

No, it isn't. Here is the example:

$\sqrt{2}$ is irrational number.

$-\sqrt{2}$ is irrational number.

And $1/\sqrt{2}$ is irrational number too.

But:

$\sqrt{2}+(-\sqrt{2})=0$ -- rational number.

$\sqrt{2}*(1/\sqrt{2})=1$ -- rational number too.