To solve the equation [tex]\(\sqrt{x+2} = 3\)[/tex] for the value of [tex]\(x\)[/tex], follow these steps:
1. Isolate the square root: The square root is already isolated in the given equation [tex]\(\sqrt{x + 2} = 3\)[/tex].
2. Square both sides: To eliminate the square root, square both sides of the equation.
[tex]\[
(\sqrt{x + 2})^2 = 3^2
\][/tex]
This simplifies to:
[tex]\[
x + 2 = 9
\][/tex]
3. Solve for [tex]\(x\)[/tex]: Subtract 2 from both sides of the equation to find the value of [tex]\(x\)[/tex].
[tex]\[
x + 2 - 2 = 9 - 2
\][/tex]
Simplifying this yields:
[tex]\[
x = 7
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is 7.
The correct answer is [tex]\( \boxed{7} \)[/tex].
