Let's break this expression down step by step:

Given: $2\sqrt{27} + 2\sqrt{3}$

1. Simplify $\sqrt{27}$: $\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}$

2. Now substitute this into the original expression: $2(3\sqrt{3}) + 2\sqrt{3}$

3. Distribute the 2: $6\sqrt{3} + 2\sqrt{3}$

4. Combine like terms: $(6 + 2)\sqrt{3} = 8\sqrt{3}$

Thus, the simplified expression is: $8\sqrt{3}$

Would you like further details or have any questions about this?

Here are five related questions:

1. How do you simplify radicals like $\sqrt{45}$?
2. What is the general method to combine terms with square roots?
3. How would you simplify $3\sqrt{12} + \sqrt{75}$?
4. What are perfect square factors, and how do they help in simplifying radicals?
5. How can you rationalize a denominator that contains a square root?

Tip: When simplifying radicals, look for the largest perfect square factor of the number inside the square root.