The expression you're looking to simplify is:

\[
\sqrt{27} + 4\sqrt{3}
\]

First, let's simplify \(\sqrt{27}\):

\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
\]

So, the expression becomes:

\[
3\sqrt{3} + 4\sqrt{3}
\]

Now, you can combine the like terms:

\[
(3 + 4)\sqrt{3} = 7\sqrt{3}
\]

Therefore, the simplified expression is:

\[
7\sqrt{3}
\]

Would you like more details or have any other questions?

Here are some related questions you might find interesting:
1. How would you simplify \(5\sqrt{12} + 2\sqrt{3}\)?
2. What is the value of \(\sqrt{75} - 2\sqrt{3}\)?
3. How do you simplify the expression \(2\sqrt{18} + \sqrt{50}\)?
4. What are the steps to simplify \(\sqrt{45} + \sqrt{20}\)?
5. How would you approach \(\sqrt{48} - 2\sqrt{12} + \sqrt{3}\)?

**Tip:** When simplifying square roots, always look for perfect square factors to reduce them to their simplest form.

Discover how to simplify the expression square root of 27 plus 4 times square root of 3 step-by-step. This problem involves simplifying square roots and combining like terms. Suitable for high school students studying algebra.

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