You provided the expression: \(\frac{2\sqrt{5}}{3 - \sqrt{2}}\). To simplify this, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of \(3 - \sqrt{2}\), which is \(3 + \sqrt{2}\).

### Steps to simplify:

\[
\frac{2\sqrt{5}}{3 - \sqrt{2}} \times \frac{3 + \sqrt{2}}{3 + \sqrt{2}} = \frac{2\sqrt{5}(3 + \sqrt{2})}{(3 - \sqrt{2})(3 + \sqrt{2})}
\]

1. **Simplify the denominator**:
   \[
   (3 - \sqrt{2})(3 + \sqrt{2}) = 3^2 - (\sqrt{2})^2 = 9 - 2 = 7
   \]

2. **Expand the numerator**:
   \[
   2\sqrt{5}(3 + \sqrt{2}) = 2\sqrt{5} \times 3 + 2\sqrt{5} \times \sqrt{2} = 6\sqrt{5} + 2\sqrt{10}
   \]

So, the expression becomes:

\[
\frac{6\sqrt{5} + 2\sqrt{10}}{7}
\]

This is the simplified form of the given expression.

### Final Answer:
\[
\frac{6\sqrt{5} + 2\sqrt{10}}{7}
\]

Would you like further details on any part of the simplification? 

Here are 5 questions that expand on this:

1. How do you rationalize a denominator?
2. What is the purpose of using the conjugate in simplification?
3. Can you always simplify a square root expression like \(\sqrt{10}\)?
4. How do you expand binomials involving square roots?
5. What happens when you square a square root?

**Tip:** When rationalizing denominators, always multiply by the conjugate of the denominator for efficient simplification.

Learn how to simplify the expression 2√5/(3 - √2) by rationalizing the denominator. This solution covers key algebraic concepts such as using the conjugate, expanding binomials, and simplifying square roots. Suitable for students in Grades 8-10.

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