Answer :
To determine which of the given expressions is equivalent to \( 60^{\frac{1}{2}} \), we can interpret \( 60^{\frac{1}{2}} \) as the square root of 60.
Here is a detailed step-by-step analysis:
1. Understand the Expression \( 60^{\frac{1}{2}} \):
- The exponent \(\frac{1}{2}\) indicates the square root. Hence, \( 60^{\frac{1}{2}} \) is the same as \( \sqrt{60} \).
2. Review the Options:
Let's compare \( 60^{\frac{1}{2}} \) with each option provided:
- \(\frac{60}{2}\):
[tex]\[\frac{60}{2} = 30.\][/tex]
Clearly, \( 60^{\frac{1}{2}} \) or \( \sqrt{60} \) is not equal to 30.
- \(\sqrt{60}\):
\(\sqrt{60}\) directly represents the square root of 60. This matches \( 60^{\frac{1}{2}} \).
- \(\frac{1}{60^2}\):
[tex]\[60^2 = 3600 \quad \text{and} \quad \frac{1}{60^2} = \frac{1}{3600}.\][/tex]
This is very different from \( 60^{\frac{1}{2}} \).
- \(\frac{1}{\sqrt{60}}\):
This represents the reciprocal of the square root of 60, i.e., \(\frac{1}{60^{\frac{1}{2}}}\). This is essentially the inverse of \( 60^{\frac{1}{2}} \).
Only \(\sqrt{60}\) is directly equivalent to \( 60^{\frac{1}{2}} \).
Therefore, the correct option is:
\(\sqrt{60}\)
This corresponds to the second option. Since indices start from 1 for the options list, the correct choice is index 2.
Here is a detailed step-by-step analysis:
1. Understand the Expression \( 60^{\frac{1}{2}} \):
- The exponent \(\frac{1}{2}\) indicates the square root. Hence, \( 60^{\frac{1}{2}} \) is the same as \( \sqrt{60} \).
2. Review the Options:
Let's compare \( 60^{\frac{1}{2}} \) with each option provided:
- \(\frac{60}{2}\):
[tex]\[\frac{60}{2} = 30.\][/tex]
Clearly, \( 60^{\frac{1}{2}} \) or \( \sqrt{60} \) is not equal to 30.
- \(\sqrt{60}\):
\(\sqrt{60}\) directly represents the square root of 60. This matches \( 60^{\frac{1}{2}} \).
- \(\frac{1}{60^2}\):
[tex]\[60^2 = 3600 \quad \text{and} \quad \frac{1}{60^2} = \frac{1}{3600}.\][/tex]
This is very different from \( 60^{\frac{1}{2}} \).
- \(\frac{1}{\sqrt{60}}\):
This represents the reciprocal of the square root of 60, i.e., \(\frac{1}{60^{\frac{1}{2}}}\). This is essentially the inverse of \( 60^{\frac{1}{2}} \).
Only \(\sqrt{60}\) is directly equivalent to \( 60^{\frac{1}{2}} \).
Therefore, the correct option is:
\(\sqrt{60}\)
This corresponds to the second option. Since indices start from 1 for the options list, the correct choice is index 2.
