The expression \( \frac{1}{\sqrt{5}} \) represents the reciprocal of the square root of 5. To simplify or rationalize this expression, you can multiply both the numerator and the denominator by \( \sqrt{5} \) to eliminate the square root from the denominator:

\[
\frac{1}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{5}}{5}
\]

So, \( \frac{1}{\sqrt{5}} \) simplifies to \( \frac{\sqrt{5}}{5} \).

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How do you rationalize the denominator of a fraction?
2. What is the significance of rationalizing a denominator?
3. How would you express \( \frac{1}{\sqrt{3}} \) in a simplified form?
4. Can you simplify \( \frac{2}{\sqrt{7}} \) similarly?
5. How does \( \frac{\sqrt{5}}{5} \) compare to \( \frac{1}{\sqrt{5}} \) in decimal form?

**Tip:** When rationalizing a denominator, the goal is to remove any square roots or other irrational numbers from the denominator to make the expression easier to work with.

Learn how to simplify \( \frac{1}{\sqrt{5}} \) by rationalizing the denominator. This involves multiplying both numerator and denominator by \( \sqrt{5} \) to eliminate the square root from the denominator, resulting in \( \frac{\sqrt{5}}{5} \). Understand the process of rationalization and its importance in simplifying algebraic expressions. Suitable for Grades 9-12 students.

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