To simplify the expression \(\frac{5}{2\sqrt{5}}\), you can follow these steps:

1. **Rationalize the denominator:** Multiply the numerator and the denominator by \(\sqrt{5}\) to get rid of the square root in the denominator.

\[
\frac{5}{2\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{5\sqrt{5}}{2 \cdot 5}
\]

2. **Simplify the fraction:** Simplify the expression by canceling out the common factor of 5 in the numerator and denominator.

\[
\frac{5\sqrt{5}}{10} = \frac{\sqrt{5}}{2}
\]

So, the simplified form of \(\frac{5}{2\sqrt{5}}\) is \(\frac{\sqrt{5}}{2}\).

Would you like a detailed explanation of the steps? Here are some related questions you might find useful:

1. How do you simplify expressions with square roots in the denominator?
2. What is the process of rationalizing the denominator?
3. Can all fractions with square roots be simplified?
4. What are some common mistakes when simplifying expressions with radicals?
5. How do you multiply and divide expressions involving square roots?

**Tip:** When simplifying fractions with square roots in the denominator, always aim to rationalize the denominator by eliminating the square root using multiplication!

Learn how to simplify the fraction 5/(2*sqrt(5)) step-by-step. This problem involves rationalizing the denominator and simplifying fractions with square roots. Suitable for high school students studying algebra and advanced mathematics.

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