Disproof by Counter Example

Example

Prove that the following statement is not true: The product of two irrational numbers is always irrational.

1. Let the two irrational numbers be $\sqrt{2}$ and $\sqrt{8}$ 1.1. Then, $\sqrt{2}\times \sqrt{8}=\sqrt{2\times 8}$ (by basic algebra), which $=\sqrt{16}=4$, which is a rational number
2. Therefore, the statement “the product of two irrational numbers is always irrational” is not true