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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.

Simplify the expression: \(\sqrt{(\sqrt{3}-3)^2} + \sqrt{(3+\sqrt{3})^2}\)

This problem demonstrates how to simplify the expression \(\sqrt{(\sqrt{3}-3)^2} + \sqrt{(3+\sqrt{3})^2}\), using properties of radicals and absolute values. Suitable for students in Grades 9-11, this solution walks through the necessary algebraic steps.

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