Question

Explain why multiplying two irrational numbers could result in either an irrational number or a rational number.

Answer 1

Because if you multiply 2 different irrational numbers (like the following)
$\sqrt{3} \times \sqrt{17}$
You will get an irrational answer.

BUT
if you multiply the same square root (which are both irrational, you get a rational number)

$\sqrt{3} \times \sqrt{3} = 3$