Question
How can you rewrite 25 1/4 using a root?(1 point)
Answers
GPT-4o mini
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.
\[
25 \frac{1}{4} = 25 + \frac{1}{4} = \frac{25 \times 4}{4} + \frac{1}{4} = \frac{100}{4} + \frac{1}{4} = \frac{101}{4}
\]
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.