To rewrite \( 8 \frac{1}{2} \) using a root, we first convert it into an improper fraction:
\[ 8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} \]
Next, we can express this fraction in terms of a square root. The expression that closely resembles \( \frac{17}{2} \) would be \( \frac{\sqrt{(17)^2}}{\sqrt{(2)^2}} \). However, to rewrite this as a cleaner root expression, we can write:
\[ 8 \frac{1}{2} \approx \sqrt{8^2 + 1} \]
Among the provided options, the one that correctly represents \( 8 \frac{1}{2} = \frac{17}{2} \) using a root is:
None of the provided responses correctly simplify or relate to \( 8 \frac{1}{2} \).
However, if you were looking for a creative way to express this, you could suggest:
- \( \sqrt{(8^2 + 1^2 \cdot 2)} \), which gives a numerical approximation but doesn't match any of the given choices exactly.