1 answer
(click or scroll down)
To express \( 5 - \sqrt{3} \) using rational exponents, we first recognize that the term \( \sqrt{3} \) can be rewritten using rational exponents.
The square root of a number can be represented as raising that number to the power of \( \frac{1}{2} \):
\[
\sqrt{3} = 3^{\frac{1}{2}}
\]
However, since the expression we are looking at is \( 5 - \sqrt{3} \), we are not looking for the exponent of \( \sqrt{3} \) directly, but rather focusing on writing \( \sqrt{3} \) with its rational exponent.
Thus, the equivalent expression to \( 5 - \sqrt{3} \) does not change the overall expression; however, the relevant part concerning the rational exponent is that:
\[
\sqrt{3} = 3^{\frac{1}{2}}
\]
So the rational exponent associated with \( \sqrt{3} \) is \( \frac{1}{2} \).
Therefore, the rational exponent you are looking for in \( 5 - \sqrt{3} \) is:
\[
\frac{1}{2}
\]