What is the product of two irrational numbers?

The product of two irrational numbers is either rational or irrational.

Example 1: 

We know that $\sqrt{2}$ and $\sqrt{3}$ are two irrational numbers.

Here, the product of these two numbers,

$\sqrt{2}\times \sqrt{3}=\sqrt{6}$, which is an irrational number.

Example 2: 

Now when we multiply $\sqrt{3}$ with itself, we get,

$\sqrt{3}\times \sqrt{3}=\sqrt{9}=3$, which is a rational number.

So, the product of two irrational numbers is either rational or irrational.