(5-2\sqrt(5))/(\sqrt(5))*(\sqrt(5))/(\sqrt(5))

Let's simplify the expression:

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

First, note that multiplying by \(\frac{\sqrt{5}}{\sqrt{5}}\) is equivalent to multiplying by 1, so it doesn't change the value of the expression. However, this multiplication simplifies the expression by rationalizing the denominator.

We can distribute \(\frac{\sqrt{5}}{\sqrt{5}}\) over the numerator:

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

Simplify each part:

- \(5 \times \sqrt{5} = 5\sqrt{5}\)
- \(\sqrt{5} \times \sqrt{5} = 5\)
- \(-2\sqrt{5} \times \sqrt{5} = -2 \times 5 = -10\)
- \(\sqrt{5} \times \sqrt{5} = 5\)

So the expression simplifies to:

\[
\frac{5\sqrt{5} - 10}{5}
\]

We can separate the terms in the numerator:

\[
\frac{5\sqrt{5}}{5} - \frac{10}{5}
\]

Simplify each term:

- \(\frac{5\sqrt{5}}{5} = \sqrt{5}\)
- \(\frac{10}{5} = 2\)

So, the simplified result is:

\[
\sqrt{5} - 2
\]

Thus, the final answer is:

\[
\boxed{\sqrt{5} - 2}
\]

Would you like more details on any step? Here are five related questions to think about:

1. How would you rationalize the denominator of \(\frac{1}{\sqrt{7}}\)?
2. What is the result of \(\frac{3 + \sqrt{2}}{\sqrt{2}}\)?
3. Can you simplify \(\frac{\sqrt{12} - \sqrt{3}}{\sqrt{3}}\)?
4. How do you simplify \(\frac{7 - \sqrt{7}}{\sqrt{7}}\)?
5. What is the process for rationalizing complex denominators like \(\frac{2}{\sqrt{3} - 1}\)?

**Tip:** When simplifying expressions with square roots, rationalizing the denominator can make the expression easier to work with.

Learn how to simplify the expression (5 - 2√5)/√5 * √5/√5 step-by-step with detailed explanations. This problem involves rational expressions and square roots. Suitable for high school students (Grades 10-12).

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