To find the length of one side of the square, we start by noting that the area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
In this case, the area is given as
\[ 16 + 8x + x^2. \]
We need to express the side length as a square root of the area. Therefore, we write:
\[ \text{side} = \sqrt{16 + 8x + x^2}. \]
Next, we will simplify \( 16 + 8x + x^2 \). We notice that the expression can be rearranged:
\[ x^2 + 8x + 16. \]
This looks like a perfect square trinomial. We can rewrite it as:
\[ (x + 4)^2. \]
Thus, we have:
\[ 16 + 8x + x^2 = (x + 4)^2. \]
Now, we take the square root of both sides to find the side length:
\[ \text{side} = \sqrt{(x + 4)^2}. \]
Since we are considering lengths, we take the principal (non-negative) square root:
\[ \text{side} = x + 4. \]
Therefore, the expression that represents the length of one side of the square is:
\[ \boxed{x + 4}. \]
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