Question

Question
Given that the meaning of a rational exponent can be connected to the meaning of a root, how can you rewrite 5–√3
using a rational exponent?(1 point)
Responses

35
3 superscript 5 baseline

53
5 cubed

513
5 superscript Start Fraction 1 over 3 End Fraction baseline

51

Answer 1

To rewrite \( 5 - \sqrt{3} \) using a rational exponent, you can focus on the square root part. The square root of a number can be expressed as a rational exponent of \( \frac{1}{2} \). Thus, \( \sqrt{3} \) can be rewritten as \( 3^{\frac{1}{2}} \).

However, your expression \( 5 - \sqrt{3} \) seems to suggest you're looking for the form of \( \sqrt{3} \) specifically under a rational exponent. Generally, the representation should be about the square root itself:

So,

\[
5 - \sqrt{3} = 5 - 3^{\frac{1}{2}}
\]

But since the question asks directly about \( \sqrt{3} \), it seems you're looking for the representation of \( \sqrt{3} \) alone in the options you've provided.

None of the provided options exactly match the expression \( 5 - \sqrt{3} \). However, if you're focusing solely on converting \( \sqrt{3} \) to a rational exponent, the option would be:

**\( 3^{\frac{1}{2}} \)**

But based on the specific choices you've provided in your question, it’s likely you needed a more specified transformation that directly references rational exponents without the negative context. If that is necessary, I would recommend verifying how the options relate to what you want to convert as \( 5 - \sqrt{3} \) wouldn’t directly be simplified further without additional context.