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.

Learn how to simplify the radical expression 2√27 + 2√3 with a step-by-step solution. This problem demonstrates key concepts in simplifying radicals and combining like terms, suitable for students in Grades 8-10.

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