Question

How can you rewrite 2514
using a root?(1 point)
Responses

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

25−−√4

Answer 1

To rewrite 2514 using a root, we can express it as follows:

2514 = 25 * 14

Now, we can use the property of square roots that states \( \sqrt{a * b} = \sqrt{a} * \sqrt{b} \). Thus, we can rewrite:

\[
2514 = 25 * 14 = \sqrt{25 * 14^2} = \sqrt{(5^2) * (14^2)} = \sqrt{25 \cdot 14^2}
\]

However, since none of the responses provided exactly match this, let's analyze them to find the most logical option based on the initial statement:

1. \( \sqrt{14} * 25 \)
2. \( \sqrt[4]{\frac{1}{25}} \)
3. \( \sqrt{\frac{1}{4}} * \sqrt{25} \)
4. \( \sqrt{25} * 4 \)

None of these exactly represent 2514 directly. If we interpret the question as seeking a combination of numbers or roots that could approximate certain simplifications in relation to \(2514\):

Given this, **none of the provided options accurately rewrites 2514 in a simplified root form** using the mathematical properties and simplifications.

You can choose to go with the most relevant match (such as option 4, but it's still not a correct match for 2514):

**Best option from interpretations:
\( \sqrt{25} \cdot 4 \)** (as a loose interpretation in the context of roots, though it equals 20 and not 2514).