Write a pair of irrational numbers whose product is rational.

Answer

To solve the question of finding a pair of irrational numbers whose product is rational, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Irrational Numbers**:
- Recall that irrational numbers cannot be expressed in the form of \( \frac{p}{q} \) where \( q \neq 0 \). Examples of irrational numbers include \( \sqrt{2} \), \( \sqrt{3} \), \( \pi \), and \( e \).

**Hint**: Remember that irrational numbers are those that cannot be expressed as fractions.

2. **Choosing Irrational Numbers**:
- Let's choose \( \sqrt{2} \) as our first irrational number. We will use it again as our second irrational number. So, we have:
- First irrational number: \( \sqrt{2} \)
- Second irrational number: \( \sqrt{2} \)

**Hint**: You can use the same irrational number twice to create a product that is rational.

3. **Calculating the Product**:
- Now, we need to find the product of these two irrational numbers:
\[ \sqrt{2} \times \sqrt{2} \]

**Hint**: Remember that multiplying two square roots can be simplified.

4. **Simplifying the Product**:
- Using the property of square roots, we can simplify the product:
\[ \sqrt{2} \times \sqrt{2} = \sqrt{2^2} = \sqrt{4} = 2 \]

**Hint**: The square root of a number squared returns the original number.

5. **Identifying the Result**:
- The result of the multiplication is \( 2 \), which is a rational number (since it can be expressed as \( \frac{2}{1} \)).

**Hint**: Check if the result can be expressed in the form \( \frac{p}{q} \) where \( q \neq 0 \).

### Final Answer:
The pair of irrational numbers whose product is rational is \( \sqrt{2} \) and \( \sqrt{2} \), and their product is \( 2 \), which is a rational number.