To solve the equation \( \sqrt{x - 6} + 2 = 3 \), we can follow these steps:
- Isolate the radical on one side of the equation:
\[ \sqrt{x - 6} = 3 - 2 \]
This simplifies to:
\[ \sqrt{x - 6} = 1 \]
- Square both sides to eliminate the square root:
\[ (\sqrt{x - 6})^2 = 1^2 \]
This gives:
\[ x - 6 = 1 \]
- Solve for \( x \):
\[ x = 1 + 6 \]
Thus:
\[ x = 7 \]
- Check the solution by substituting \( x = 7 \) back into the original equation:
\[ \sqrt{7 - 6} + 2 = 3 \]
This simplifies to:
\[ \sqrt{1} + 2 = 3 \]
Which is:
\[ 1 + 2 = 3 \]
Since this statement is true, the solution is valid.
Therefore, the final answer is:
\[ \boxed{7} \]