Write a pair of irrational numbers whose difference is rational.

Answer

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

### Step 1: Identify two irrational numbers
Let's choose two irrational numbers. A good choice is:
- \( a = \sqrt{5} + 3 \)
- \( b = \sqrt{5} - 3 \)

### Step 2: Calculate the difference
Now, we need to find the difference between these two numbers:
\[ a - b = (\sqrt{5} + 3) - (\sqrt{5} - 3) \]

### Step 3: Simplify the expression
Now, simplify the expression:
\[ a - b = \sqrt{5} + 3 - \sqrt{5} + 3 \]
Notice that the \( \sqrt{5} \) terms cancel each other out:
\[ a - b = 3 + 3 = 6 \]

### Step 4: Determine if the result is rational
The result \( 6 \) is a rational number since it can be expressed in the form \( \frac{6}{1} \).

### Conclusion
Thus, the pair of irrational numbers we found is \( \sqrt{5} + 3 \) and \( \sqrt{5} - 3 \), and their difference \( 6 \) is indeed a rational number.

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