To rationalize the denominator of $\frac{1}{\sqrt{3}}$, follow these steps:

Step 1: Multiply numerator and denominator by $\sqrt{3}$

To eliminate the square root from the denominator, multiply both numerator and denominator by $\sqrt{3}$:

$\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}$

Step 2: Simplify the denominator

Using the property $\sqrt{a} \cdot \sqrt{a} = a$, simplify the denominator:

$\frac{\sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{3}}{3}$

Final Answer:

$\frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$

Would you like to see more examples or further explanations? Here are related questions to explore:

1. Why do we rationalize denominators, and when is it necessary?
2. How do you rationalize denominators with higher roots, like cube roots?
3. What happens if the denominator has two terms, such as $1 / (\sqrt{3} + 1)$?
4. How can you verify that rationalizing the denominator does not change the value of the fraction?
5. Can the process of rationalizing be reversed?

Tip: Always ensure the denominator is free of square roots or other irrational terms to make expressions easier to work with in further calculations.