To rewrite \( 25 \frac{1}{4} \) using a root, start by converting the mixed number to an improper fraction:
\[ 25 \frac{1}{4} = 25 + \frac{1}{4} = \frac{25 \times 4}{4} + \frac{1}{4} = \frac{100}{4} + \frac{1}{4} = \frac{101}{4} \]
Next, you can express 25 as a square:
\[ 25 = 5^2 \]
Thus, we can write:
\[ 25 \frac{1}{4} = 5^2 + \frac{1}{4} \]
To write this in terms of a root, note that \( \frac{1}{4} \) can be expressed as \( \left( \frac{1}{2} \right)^2 \):
Putting this together, you can express \( \frac{101}{4} \) using square roots:
\[ 25 \frac{1}{4} = \frac{(5^2) + (1/2)^2}{1} \]
However, this doesn't fully encapsulate rooting. Instead, if we want to express more generally:
\[ 25 \frac{1}{4} = \sqrt{(25 \cdot 4) + 1} = \sqrt{101} \]
While it could also simply be seen as \( 5\sqrt{1} + \frac{1}{4} \).
In a structured way, simplifying leads to stating:
\[ 25 \frac{1}{4} = \sqrt{(5^2) + (0.5^2)} \]
Ultimately:
\[ 25 \frac{1}{4} \approx \sqrt{101} , (as an approximate root) \]
If more specific interpretation is needed, please clarify. But possibly depending on context, \(25 \frac{1}{4} \rightarrow 5 \sqrt{5} + 0.5\) or simply rephrased as "using square root" approach.
However, in equation form:
\[ x = 5 + \frac{1}{2}, \text{where x is representing mixed number in roots.} \]
Overall, keeping contextual clarity may lead different mathematical interpretations.