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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.

Learn how to simplify the expression (sqrt(x) + 3)^2 using the binomial expansion method. Explore step-by-step solutions and explanations, including the application of the binomial expansion formula and handling square roots in algebraic expressions. Suitable for high school students.

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