Question

Write the radical form of the expression 25 1/4
25 1/4

Answer 1

To express \( 25 \frac{1}{4} \) in radical form, first, we need to convert the mixed number into an improper fraction.

1. Convert \( 25 \frac{1}{4} \) to an improper fraction:
\[
25 \frac{1}{4} = 25 + \frac{1}{4} = \frac{25 \times 4}{4} + \frac{1}{4} = \frac{100 + 1}{4} = \frac{101}{4}
\]

2. Now, express \( \frac{101}{4} \) in radical form:
\[
\frac{101}{4} = \frac{101}{2^2}
\]

To express this in radical form:
\[
= \frac{101}{2^2} = \frac{101}{\sqrt{4}} = \frac{101}{2}
\]
or,
\[
= \sqrt{\frac{101^2}{4}} = \frac{\sqrt{101^2}}{2} = \frac{101}{2}
\]

So, the radical form of \( 25 \frac{1}{4} \) could be expressed as \( \frac{101}{2} \) or simply as the original fraction represented without radicals. However, if you want to keep it purely in terms of roots, you can show the process of taking the square root as mentioned.

If you meant the direct square root representation of the original mixed number, you can also say:

\[
\sqrt{25 \frac{1}{4}} = \sqrt{\frac{101}{4}} = \frac{\sqrt{101}}{2}
\]

So, depending on what form you're looking for, you can express \( 25 \frac{1}{4} \) as either of these forms:
- \( \frac{101}{4} \)
- \( \frac{101}{2} \)
- or \(\sqrt{25.25} = \frac{\sqrt{101}}{2}\).