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.