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

513
5 superscript Start Fraction 1 over 3 End Fraction baseline

51
5 superscript 1 baseline

53
5 cubed

35

Answer 1

To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we need to focus on the square root and how it relates to rational exponents. The square root of a number can be expressed with a rational exponent as follows:

\[
\sqrt{a} = a^{\frac{1}{2}}
\]

However, the expression \( 5 - \sqrt{3} \) itself doesn't directly translate into a rational exponent only for the square root. If we were to focus solely on the square root component, we could write:

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

But since the whole expression \( 5 - \sqrt{3} \) is being asked to be rewritten, it seems there might be a misunderstanding about changing expressions directly including negative signs or basic arithmetic.

From the responses you provided, none of them directly relate to the use of a rational exponent in the context of a subtraction in the original expression.

Please clarify if you're specifically looking to express just the square root term (like \( \sqrt{3} \)) or otherwise specify another related expression. If it’s the root specifically:

\( \sqrt{3} = 3^{\frac{1}{2}} \)

If focusing on rewriting as a whole, we can't correctly transform \( 5 - \sqrt{3} \) into a simple rational exponent without context.

So the answer regarding how to express the square root term is:

3^{\frac{1}{2}}

If we are restructuring the whole expression, the mathematical representation may remain as is unless stated otherwise.