Write of pair of irrational numbers whose difference is irrational .

Answer

To solve the problem of finding a pair of irrational numbers whose difference is also irrational, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Two Irrational Numbers**:
Let's choose the irrational numbers:
- \( a = \sqrt{3} + 2 \)
- \( b = \sqrt{2} - 3 \)

2. **Calculate the Difference**:
We need to find the difference between these two numbers:
\[ a - b = (\sqrt{3} + 2) - (\sqrt{2} - 3) \]

3. **Simplify the Expression**:
Distributing the negative sign in the second term:
\[ a - b = \sqrt{3} + 2 - \sqrt{2} + 3 \]
Combine like terms:
\[ a - b = \sqrt{3} - \sqrt{2} + 5 \]

4. **Determine the Nature of the Result**:
We need to confirm that the result \( \sqrt{3} - \sqrt{2} + 5 \) is irrational. Since both \( \sqrt{3} \) and \( \sqrt{2} \) are irrational numbers, their difference \( \sqrt{3} - \sqrt{2} \) is also irrational. Adding a rational number (5) to an irrational number results in an irrational number.

5. **Final Conclusion**:
Therefore, the difference \( a - b = \sqrt{3} - \sqrt{2} + 5 \) is irrational. Thus, we have found a pair of irrational numbers whose difference is also irrational.

### Final Answer:
The pair of irrational numbers is \( \sqrt{3} + 2 \) and \( \sqrt{2} - 3 \), and their difference is irrational.

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