To rewrite \( 25 \frac{1}{4} \) using a root, we can express the mixed number as an improper fraction first.
\[ 25 \frac{1}{4} = \frac{25 \times 4 + 1}{4} = \frac{100 + 1}{4} = \frac{101}{4} \]
Then, we can express \( \frac{101}{4} \) using a square root:
\[ = \frac{1}{4} \cdot 101 = \frac{101}{2^2} = \frac{\sqrt{101}}{\sqrt{4}} = \sqrt{\frac{101}{4}} \]
However, this does not directly match with your options.
If we're looking to express \( 25 \frac{1}{4} \) in its simplest form, it can also be seen intuitively:
25 can be expressed as \( \sqrt{625} \), since \( 625 = 25^2 \).
Putting this all together simply, you can see that the most simplified root representation does not correspond directly to your answer choices. However, the closest representation in terms of roots is:
\[ \sqrt{25 \cdot \frac{101}{4}} \]
Without more context about the answer choices you've provided, it seems none of them directly represent this mixed number effectively as a root representation.
Please let me know if you have further details or context about how this should be represented!
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