Simplify the radical expression.

To simplify the expression \( 62 - \sqrt{514} \), we first need to rewrite \( \sqrt{514} \).

1. Factor \( 514 \) to check if it can be simplified.
- \( 514 = 2 \times 257 \)

2. Since \( 257 \) is a prime number, we cannot simplify \( \sqrt{514} \) further. We can approximate \( \sqrt{514} \) if needed for numerical evaluation, but for now, we keep it in radical form.

Now, let's look at the expression:

\[
62 - \sqrt{514}
\]

Since \( 514 \) does not simplify further, the expression remains as

\[
62 - \sqrt{514}
\]

To provide the answer in the simplified form among the options you provided, we now evaluate the numerical approximation of \( \sqrt{514} \):

\[
\sqrt{514} \approx 22.7
\]
Thus,
\[
62 - \sqrt{514} \approx 62 - 22.7 \approx 39.3
\]

None of the options provided seem to match this computation perfectly.

However, let's check the possible options.

1. **\[ 32\sqrt{7} \]**
2. **\[ 60 \sqrt{7} \]**
3. **\[ 2\sqrt{7} \]**
4. **\[ 30\sqrt{7} \]**

Since we can't directly simplify \( 62 - \sqrt{514} \) into these forms cleanly without further context, I will indicate that the question seems incomplete or has missing context, as the radical expression itself simplifies only as discussed above.

None of the provided options is correct without further clarification on the task at hand. If we had to match the value closely, the most reasonable choice might depend on knowing what values each option provides numerically.

Please provide any additional information or clarity on the original expression if available!