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We are asked to find which expression results in a rational number. Let's analyze each option:

### Option A: \( \sqrt{2} \cdot \sqrt{18} \)
Using the property of square roots, \( \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \):
\[
\sqrt{2} \cdot \sqrt{18} = \sqrt{2 \cdot 18} = \sqrt{36} = 6
\]
Since 6 is a rational number, **A** is the correct answer.

### Option B: \( 5 \cdot \sqrt{5} \)
This expression results in \( 5\sqrt{5} \), which is irrational because \( \sqrt{5} \) is irrational, and multiplying it by 5 does not make it rational.

### Option C: \( \sqrt{2} + \sqrt{2} \)
This simplifies to \( 2\sqrt{2} \), which is irrational because \( \sqrt{2} \) is irrational, and multiplying it by 2 does not make it rational.

### Option D: \( 3\sqrt{2} + 2\sqrt{3} \)
Both \( \sqrt{2} \) and \( \sqrt{3} \) are irrational, so adding these terms results in an irrational number.

### Conclusion:
The only expression that results in a rational number is **A: \( \sqrt{2} \cdot \sqrt{18} = 6 \)**.

Would you like further explanation or have any questions?

### Related Questions:
1. What makes a number rational or irrational?
2. How do you multiply or add square roots?
3. How do properties of square roots simplify complex expressions?
4. Can multiplying an irrational number by a rational number ever result in a rational number?
5. What are some common irrational numbers?

**Tip:** Multiplying two square roots can simplify into a rational number if the product of the numbers inside the square roots is a perfect square.

Which expression results in a rational number?

Analyze expressions involving square roots to determine which one results in a rational number. This problem covers key concepts such as multiplying square roots and identifying rational and irrational numbers. Suitable for students in Grades 8-10.

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