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Let's walk through the solution to this problem step-by-step.

### Problem:
Rationalize the denominator of:
\[
\frac{2}{5 - \sqrt{20}}
\]

### Step 1: Multiply by the Conjugate
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of \(5 - \sqrt{20}\), which is \(5 + \sqrt{20}\).

\[
\frac{2}{5 - \sqrt{20}} \times \frac{5 + \sqrt{20}}{5 + \sqrt{20}}
\]

### Step 2: Expand the Numerator and Denominator
Using the distributive property:

- **Numerator**: \(2 \cdot (5 + \sqrt{20})\)
  \[
  2(5 + \sqrt{20}) = 10 + 2\sqrt{20}
  \]

- **Denominator**: \((5 - \sqrt{20})(5 + \sqrt{20})\)  
  This is a difference of squares:
  \[
  (5)^2 - (\sqrt{20})^2 = 25 - 20 = 5
  \]

So, the expression becomes:
\[
\frac{10 + 2\sqrt{20}}{5}
\]

### Step 3: Simplify the Result
Now, simplify the numerator by factoring out 2 from both terms:
\[
\frac{2(5 + \sqrt{20})}{5}
\]

We can also simplify \(\sqrt{20}\):
\[
\sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5}
\]
So, the expression becomes:
\[
\frac{2(5 + 2\sqrt{5})}{5}
\]

### Step 4: Distribute and Final Simplified Form
Distribute the 2:
\[
\frac{10 + 4\sqrt{5}}{5}
\]

Now, split the fraction:
\[
\frac{10}{5} + \frac{4\sqrt{5}}{5} = 2 + \frac{4\sqrt{5}}{5}
\]

### Final Answer:
\[
2 + \frac{4\sqrt{5}}{5}
\]

Let me know if you have questions or need further details!

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Here are 5 related questions you might explore:
1. How do you find the conjugate of a binomial involving square roots?
2. What is the difference of squares formula, and when is it useful?
3. How do you simplify square roots such as \(\sqrt{20}\)?
4. What are other examples of rationalizing denominators?
5. How can you multiply and simplify expressions involving radicals?

**Tip:** When dealing with square roots, always look for perfect squares inside the radical to simplify them!

Rationalize the denominator of \( \frac{2}{5 - \sqrt{20}} \). Simplify your answer completely.

Learn how to rationalize the denominator of \( \frac{2}{5 - \sqrt{20}} \) and simplify the expression completely. This solution covers concepts such as rationalizing denominators, simplifying radicals, and using the difference of squares. Ideal for students in Grades 10-12.

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