The expression provided is:

$(\sqrt{x} + 3)^2$

To simplify this, we will use the binomial expansion formula $(a + b)^2 = a^2 + 2ab + b^2$, where $a = \sqrt{x}$ and $b = 3$.

Let's expand it:

1. Square the first term: $(\sqrt{x})^2 = x$

2. Multiply the two terms and then double the result: $2 \times \sqrt{x} \times 3 = 6\sqrt{x}$

3. Square the second term: $3^2 = 9$

4. Combine all the terms: $(\sqrt{x} + 3)^2 = x + 6\sqrt{x} + 9$

Thus, the fully simplified form of the given expression is:

$x + 6\sqrt{x} + 9$

Would you like more details on any step? Here are some questions to expand your understanding:

1. What is the binomial expansion formula for $(a + b)^2$?
2. How do you simplify the square of a square root?
3. What is the significance of the middle term in the expansion $(\sqrt{x} + 3)^2$?
4. How can you apply this expansion technique to other expressions?
5. What would happen if the expression was $(\sqrt{x} - 3)^2$ instead?

Tip: When expanding a binomial square, always ensure that each term is properly squared and that the middle term is doubled. This will help avoid common mistakes in expansion.