To find an expression equivalent to [tex]\(60^{\frac{1}{2}}\)[/tex], let's understand what [tex]\(60^{\frac{1}{2}}\)[/tex] represents.
The expression [tex]\(60^{\frac{1}{2}}\)[/tex] is asking for the square root of 60. In mathematical notation, the square root of 60 is written as:
[tex]\[
\sqrt{60}
\][/tex]
None of the other options match this description:
- [tex]\(\frac{60}{2}\)[/tex] simplifies to 30, which is not equivalent to [tex]\(\sqrt{60}\)[/tex].
- [tex]\(\frac{1}{60^2}\)[/tex] simplifies to [tex]\(\frac{1}{3600}\)[/tex], which is clearly not the square root of 60.
- [tex]\(\frac{1}{\sqrt{60}}\)[/tex] is the reciprocal of the square root of 60, not the square root itself.
Therefore, the expression that is equivalent to [tex]\(60^{\frac{1}{2}}\)[/tex] is:
[tex]\[
\sqrt{60}
\][/tex]
This can also be confirmed by evaluating the numerical value of [tex]\(\sqrt{60}\)[/tex], which is approximately 7.745966692414834. This is indeed the correct interpretation and matches the value expected from the square root of 60.
Hence, the correct answer is:
[tex]\[
\sqrt{60}
\][/tex]
