To simplify the expression \( \sqrt{510} + \sqrt{10} \), we can start by rewriting \( \sqrt{510} \).
First, notice that:
\[ \sqrt{510} = \sqrt{51 \times 10} = \sqrt{51} \cdot \sqrt{10} \]
Now the expression becomes:
\[ \sqrt{510} + \sqrt{10} = \sqrt{51} \cdot \sqrt{10} + \sqrt{10} \]
We can factor out \( \sqrt{10} \):
\[ \sqrt{10}(\sqrt{51} + 1) \]
This gives us the sum of the square roots, but does not resolve to any of the provided answers. Since none of the options seem to simplify to a closed form that can be recognized, let’s check if \( \sqrt{510} + \sqrt{10} \) could match with the presented options, potentially through numerical approximation or other algebraic manipulations.
However, looking at the options you provided:
- \( 6\sqrt{10} \)
- \( \sqrt{25} \)
- \( \sqrt{60} \)
- \( \sqrt{620} \)
None naturally correspond through straightforward simplifications or transformations. As such, the expression could potentially remain in the recognizable form we factored.
If any further transformation is meant specifically to link to the options provided or clearer definitions of what's expected, please clarify.
Given purely based on algebra, the correct answer is not represented in your options. Thus, the final answer could best be approximated numerically as:
\[ \sqrt{510} \approx 22.58 \quad \text{and} \quad \sqrt{10} \approx 3.16 \]
\[ \sqrt{510} + \sqrt{10} \approx 22.58 + 3.16 \approx 25.74 \]
Thus, a non-approximate answer closely resembling is simply \( \sqrt{10}(\sqrt{51}+1) \).
Again, please clarify if other computations or transformations are intended!