Question

How can you rewrite 25 1/4 using a root?(1 point)

Answer 1

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.