prove that `sqrt(3)-sqrt(2)` is an irrational number.

Explanation

To prove that \( \sqrt{3} - \sqrt{2} \) is an irrational number, we will use a proof by contradiction. Here are the steps:

### Step 1: Assume the contrary
Assume that \( \sqrt{3} - \sqrt{2} \) is a rational number. Let's denote it as \( x \):
\[ x = \sqrt{3} - \sqrt{2} \]

...