To solve the problem, we need to identify the equivalent mathematical expression for [tex]\( BO^{\frac{1}{2}} \)[/tex].
### Step-by-Step Solution:
1. Understanding the Expression:
- [tex]\( BO^{\frac{1}{2}} \)[/tex] refers to the square root of [tex]\( BO \)[/tex]. In mathematical terms, [tex]\( BO^{\frac{1}{2}} \)[/tex] is written as [tex]\( \sqrt{BO} \)[/tex].
2. Given Value of [tex]\( BO \)[/tex]:
- We are given that [tex]\( BO \)[/tex] is 60.
3. Calculate the Equivalent Expression:
- Therefore, [tex]\( BO^{\frac{1}{2}} = \sqrt{60} \)[/tex].
4. Evaluate the Provided Options:
- Option 1: [tex]\( \frac{60}{2} \)[/tex]
[tex]\[
\frac{60}{2} = 30 \quad \text{(This is not equivalent to \( \sqrt{60} \))}
\][/tex]
- Option 2: [tex]\( \sqrt{60} \)[/tex]
[tex]\[
\sqrt{60} \approx 7.745966692414834 \quad \text{(This is the value of \( BO^{\frac{1}{2}} \))}
\][/tex]
- Option 3: [tex]\( \frac{1}{60^2} \)[/tex]
[tex]\[
\frac{1}{60^2} = \frac{1}{3600} \quad \text{(This is not equivalent to \( \sqrt{60} \))}
\][/tex]
- Option 4: [tex]\( \frac{1}{\sqrt{60}} \)[/tex]
[tex]\[
\frac{1}{\sqrt{60}} = \frac{1}{7.745966692414834} \approx 0.12909944487358055 \quad \text{(This is not equivalent to \( \sqrt{60} \))}
\][/tex]
5. Conclusion:
- Among the options, the correct answer is:
[tex]\[
\sqrt{60}
\][/tex]
Therefore, [tex]\( BO^{\frac{1}{2}} \)[/tex] is equivalent to [tex]\( \sqrt{60} \)[/tex]. The correct option is:
[tex]\[
\boxed{\sqrt{60}}
\][/tex]
