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Let's simplify \( 3\sqrt{3} + 3\sqrt{12} \):

1. Start with \( \sqrt{12} \):  
   \[
   \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}.
   \]

2. Substitute \( \sqrt{12} \) back into the expression \( 3\sqrt{3} + 3\sqrt{12} \):  
   \[
   3\sqrt{3} + 3\sqrt{12} = 3\sqrt{3} + 3(2\sqrt{3}).
   \]

3. Simplify:  
   \[
   3\sqrt{3} + 6\sqrt{3} = 9\sqrt{3}.
   \]

### Final Answer:  
\[
\boxed{9\sqrt{3}}
\]

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Would you like further clarification or another example?

### Related Questions:  
1. How do you simplify radicals like \( \sqrt{20} \) or \( \sqrt{18} \)?  
2. What are the steps to add or subtract like terms with radicals?  
3. How do you multiply two terms involving radicals, e.g., \( (2\sqrt{3})(3\sqrt{6}) \)?  
4. How do you simplify expressions like \( 5\sqrt{27} - 2\sqrt{12} \)?  
5. What is the process for rationalizing a denominator like \( \frac{5}{\sqrt{3}} \)?  

### Tip:  
Always simplify square roots by factoring out perfect squares to make calculations easier.

Learn how to fully simplify the expression 3√3 + 3√12 with detailed steps. This problem involves simplifying square roots and combining like radical terms. Suitable for students in Grades 8-10 learning algebra and radical expressions.

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