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

3 answers

To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we need to focus specifically on the term \( \sqrt{3} \).

The square root of 3 can be expressed with a rational exponent as: \[ \sqrt{3} = 3^{1/2} \]

Therefore, \( 5 - \sqrt{3} \) can be rewritten as: \[ 5 - 3^{1/2} \]

However, if the question is specifically about how to express \( \sqrt{3} \) with a rational exponent (regardless of the entire expression), we would denote it as \( 3^{1/2} \).

Among the provided options, the one that expresses \( 5^{\text{something}} \) with a rational exponent doesn't actually apply here because \( 5 \) is not related to \( \sqrt{3} \) in terms of manipulation.

If you are looking for an expression that includes the square root in a simplified rational exponent form:

  • The correct representation of \( \sqrt{3} \) is \( 3^{1/2} \).

There is no option that directly corresponds to \( 5 - \sqrt{3} \) being rewritten accurately without further context.

Please clarify if you need something else!

choose the best one please

Based on your question and the given options, the best option to rewrite \( \sqrt{3} \) using a rational exponent would be:

\( 3^{1/2} \)

However, there's no explicit option for that. Given the provided responses, if you're looking for an expression related to \( 5 \), the closest relevant choice is:

\( 5^{1/3} \)

This option, while not directly relevant to \( \sqrt{3} \), uses a rational exponent format and is one of the suggested options given.

If your question specifically involves expressing \( 5 - \sqrt{3} \) or \( \sqrt{3} \) with rational exponents and looking specifically for \( 5^{\text{something}} \), then \( 5^{1/3} \) is technically the best choice from the options provided, even though it doesn't alter the premise of \( \sqrt{3} \).