The given function is:

\[
F(x) = \sqrt{3x + 6}
\]

### Domain of the function:
Since the square root function is only defined for non-negative values, we need to ensure that the expression inside the square root is greater than or equal to zero.

\[
3x + 6 \geq 0
\]

Solve for \( x \):

\[
3x \geq -6
\]
\[
x \geq -2
\]

Thus, the domain of the function is:

\[
x \in [-2, \infty)
\]

### Simplified Form:
This is already in its simplest form, as it's a square root function.

Would you like to know more details or have any questions about this?

Here are 5 related questions to explore:

1. What is the range of \( F(x) = \sqrt{3x + 6} \)?
2. How do you graph \( F(x) = \sqrt{3x + 6} \)?
3. How would the function change if we added a constant outside the square root, like \( F(x) = \sqrt{3x + 6} + 2 \)?
4. Can you find the inverse of \( F(x) = \sqrt{3x + 6} \)?
5. How do you compute \( F(2) \) for this function?

**Tip:** Always check the domain first for functions involving square roots to avoid undefined values.

Explore the domain and simplified form of the square root function F(x) = √(3x + 6). This problem demonstrates how to find the domain by ensuring non-negative values under the square root. Ideal for Grades 9-11, it covers key algebraic concepts.

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