How can you rewrite 25 1/4

Question

using a root?(1 point)
Responses

25−−√14
root index Start Fraction 1 over 4 End Fraction Start Root 25 End Root

14−−√25
root index 25 Start Root Start Fraction 1 over 4 End Fraction End Root

254−−−√1
root index 1 Start Root 25 superscript 4 baseline End Root

25−−√4

Answer 1

To rewrite \( 25 \frac{1}{4} \) using a root, we can express it as follows:

1. First, convert \( 25 \frac{1}{4} \) to an improper fraction:

\[ 25 \frac{1}{4} = \frac{25 \cdot 4 + 1}{4} = \frac{100 + 1}{4} = \frac{101}{4} \]

2. Now recognize that \( 25 \) can be written as \( 5^2 \). Therefore, we have:

\[ 25 \frac{1}{4} = \frac{25^{1}}{4^{1}} = \frac{(5^2)^{1/4}}{1^{1}} = 5^{2/4} = 5^{1/2} = \sqrt{5} \]

However, this doesn't strictly translate to the options provided.

Let's analyze the closest option from what's given:

The best way to express \( 25 \frac{1}{4} \) using roots in the context of the options provided is:

\[ \text{root index } \frac{1}{4} \text{ root of } 25 \quad \text{which is} \quad \sqrt[4]{25} \]

Thus, the correct response corresponding to rewriting \( 25 \frac{1}{4} \) using a root is:

root index Start Fraction 1 over 4 End Fraction Start Root 25 End Root.