Write a pair of irrational numbers whose sum is rational .

Answer

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

### Step 1: Understand the Definitions
First, we need to understand what rational and irrational numbers are.
- **Rational Numbers**: Numbers that can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).
- **Irrational Numbers**: Numbers that cannot be expressed in the form \( \frac{p}{q} \).

### Step 2: Choose Two Irrational Numbers
We need to choose two irrational numbers. A good choice is:
- \( \sqrt{3} \) (which is irrational)
- \( 4 - \sqrt{3} \) (which is also irrational)

### Step 3: Add the Two Numbers
Now, we will add these two irrational numbers together:
\[ \sqrt{3} + (4 - \sqrt{3}) \]

### Step 4: Simplify the Expression
When we simplify the expression:
\[ \sqrt{3} + 4 - \sqrt{3} \]
The \( \sqrt{3} \) and \( -\sqrt{3} \) cancel each other out:
\[ 0 + 4 = 4 \]

### Step 5: Check if the Result is Rational
The result of the addition is \( 4 \), which is a rational number since it can be expressed as \( \frac{4}{1} \).

### Final Answer
Thus, the pair of irrational numbers \( \sqrt{3} \) and \( 4 - \sqrt{3} \) has a sum that is rational (which is \( 4 \)).

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