Write a pair of irrational numbers whose product is irrational.

Answer

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

### Step 1: Define Irrational Numbers
First, we need to understand what irrational numbers are. Irrational numbers are numbers that cannot be expressed as a fraction of two integers (p/q form). Examples include numbers like √2, √3, π, etc.

### Step 2: Choose a Pair of Irrational Numbers
Let's choose two irrational numbers. We can select:
- \( \sqrt{2} \)
- \( \sqrt{3} \)

### Step 3: Multiply the Chosen Numbers
Now, we will multiply these two irrational numbers:
\[ \sqrt{2} \times \sqrt{3} \]

### Step 4: Simplify the Product
Using the property of square roots, we can simplify the product:
\[ \sqrt{2} \times \sqrt{3} = \sqrt{2 \times 3} = \sqrt{6} \]

### Step 5: Determine if the Result is Irrational
Next, we need to check if \( \sqrt{6} \) is an irrational number. Since 6 cannot be expressed as a perfect square, \( \sqrt{6} \) is indeed an irrational number.

### Final Answer
Thus, the pair of irrational numbers \( \sqrt{2} \) and \( \sqrt{3} \) has a product \( \sqrt{6} \), which is also irrational.

### Summary
The pair of irrational numbers whose product is irrational is:
- \( \sqrt{2} \) and \( \sqrt{3} \)

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