To add the square roots \( \sqrt{510} + \sqrt{10} \), we can simplify \( \sqrt{510} \) first:
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Break down \( 510 \) into its prime factors: \[ 510 = 2 \times 3 \times 5 \times 17 \] This does not have any square factors that can be simplified, so \( \sqrt{510} \) remains as is.
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Next, we look at \( \sqrt{10} \): \[ \sqrt{10} = \sqrt{10} \]
Since the square roots cannot be combined because they are not like terms, we leave the expression as:
\[ \sqrt{510} + \sqrt{10} \]
None of the provided options match in total, but if substituting for numerical approximations: \[ \sqrt{510} \approx 22.6 \quad \text{and} \quad \sqrt{10} \approx 3.16 \] which sums to about \( 25.76 \).
Now, let’s look at the options:
- \( \sqrt{620} \)
- \( \sqrt{60} \)
- \( \sqrt{25} \)
- \( \sqrt{610} \)
None of these appear directly relevant.
However, we can say that the sum is \( \sqrt{510} + \sqrt{10} \), which does not directly simplify into any of the provided responses.
If you need to pick one, note that \( \sqrt{100} = 10 \) (i.e., \( \sqrt{25} \)), but that’s not exactly the sum of those square roots. Thus, none of the responses represent the sum accurately as originally expressed.
Therefore, the most accurate choice would be to say that the sum is unseen among existing options.
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