Write a pair of irrational number whose product is rational.

Answer

To find a pair of irrational numbers whose product is rational, we can follow these steps:

### Step 1: Identify Two Irrational Numbers
Let's choose:
- \( a = \sqrt{3} + \sqrt{2} \)
- \( b = \sqrt{3} - \sqrt{2} \)

### Step 2: Verify that Both Numbers are Irrational
Both \( \sqrt{3} \) and \( \sqrt{2} \) are known to be irrational numbers. Therefore, both \( a \) and \( b \) are irrational since they are sums and differences of irrational numbers.

### Step 3: Calculate the Product of the Two Numbers
Now, we will calculate the product \( a \times b \):
\[ a \times b = (\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2}) \]

### Step 4: Apply the Difference of Squares Formula
Using the difference of squares formula, \( (x + y)(x - y) = x^2 - y^2 \), we can rewrite the product:
\[ a \times b = (\sqrt{3})^2 - (\sqrt{2})^2 \]

### Step 5: Simplify the Expression
Now, we simplify:
\[ (\sqrt{3})^2 = 3 \quad \text{and} \quad (\sqrt{2})^2 = 2 \]
Thus, we have:
\[ a \times b = 3 - 2 = 1 \]

### Conclusion
The product of the two irrational numbers \( a \) and \( b \) is \( 1 \), which is a rational number. Therefore, the pair of irrational numbers \( \sqrt{3} + \sqrt{2} \) and \( \sqrt{3} - \sqrt{2} \) satisfies the condition.

### Final Answer
The pair of irrational numbers whose product is rational is:
- \( \sqrt{3} + \sqrt{2} \)
- \( \sqrt{3} - \sqrt{2} \)

---