You have provided an expression involving radicals and their squares. Let's simplify it step-by-step:

The given expression is: $\sqrt{(\sqrt{3}-3)^2} + \sqrt{(3+\sqrt{3})^2}$

We can simplify the squares inside the square roots first:

1. $(\sqrt{3}-3)^2 = (\sqrt{3})^2 - 2 \times \sqrt{3} \times 3 + 3^2 = 3 - 6\sqrt{3} + 9$
2. $(3+\sqrt{3})^2 = 3^2 + 2 \times 3 \times \sqrt{3} + (\sqrt{3})^2 = 9 + 6\sqrt{3} + 3$

So the expression becomes: $\sqrt{3 - 6\sqrt{3} + 9} + \sqrt{9 + 6\sqrt{3} + 3}$

However, since the terms inside the square roots are perfect squares of the original binomials: $\sqrt{(\sqrt{3}-3)^2} = |\sqrt{3} - 3| \quad \text{and} \quad \sqrt{(3+\sqrt{3})^2} = |3 + \sqrt{3}|$

The absolute values resolve as:

1. $|\sqrt{3} - 3| = 3 - \sqrt{3}$ since $3 > \sqrt{3}$
2. $|3 + \sqrt{3}| = 3 + \sqrt{3}$

Therefore, the simplified expression is: $3 - \sqrt{3} + 3 + \sqrt{3} = 6$

The final answer is $\boxed{6}$.

Would you like more details on any of these steps, or do you have any other questions? Here are some related questions to consider:

1. What would the result be if the terms inside the radicals were not perfect squares?
2. How does the concept of absolute value play a role in simplifying expressions involving square roots?
3. What are other examples of expressions where simplification involves removing square roots?
4. Can you simplify $\sqrt{(2-\sqrt{2})^2} + \sqrt{(2+\sqrt{2})^2}$?
5. What is the general formula for simplifying $\sqrt{(a+b)^2}$?

Tip: When dealing with expressions involving square roots, always consider simplifying under the radical before taking the square root, as it can significantly reduce the complexity of the expression.