To simplify the expression $\frac{\sqrt{3}}{3} + \sqrt{3}$, follow these steps:

Step 1: Factor out $\sqrt{3}$

The common term is $\sqrt{3}$, so factor it out: $\frac{\sqrt{3}}{3} + \sqrt{3} = \sqrt{3} \left( \frac{1}{3} + 1 \right)$

Step 2: Simplify inside the parentheses

$\frac{1}{3} + 1 = \frac{1}{3} + \frac{3}{3} = \frac{4}{3}$

Step 3: Multiply by the common factor

$\sqrt{3} \left( \frac{4}{3} \right) = \frac{4\sqrt{3}}{3}$

Final Answer:

$\frac{4\sqrt{3}}{3}$

Let me know if you'd like further clarification! Here are some follow-up questions:

1. How do you simplify fractions with square roots?
2. What is the importance of factoring in simplifying expressions?
3. How does this concept apply to rationalizing denominators?
4. Can this method be used to simplify complex expressions involving square roots?
5. What are real-world applications of simplifying square root expressions?

Tip: Always check for common factors to simplify expressions efficiently.