To simplify the expression \( \sqrt{x^2 + 8x + 16} \), we can first recognize that the expression inside the square root is a perfect square trinomial.
We can factor \( x^2 + 8x + 16 \) as follows:
\[ x^2 + 8x + 16 = (x + 4)^2 \]
Now, substituting this back into the square root gives us:
\[ \sqrt{x^2 + 8x + 16} = \sqrt{(x + 4)^2} \]
The square root of a square is the absolute value of the original expression, so we have:
\[ \sqrt{(x + 4)^2} = |x + 4| \]
Thus, the simplified result is:
\[ \sqrt{x^2 + 8x + 16} = |x + 4| \]