To add \( \sqrt{321} + \sqrt{721} \), let's first simplify each square root:
-
Simplifying \( \sqrt{321} \):
- \( 321 = 3 \times 107 \) (neither \( 3 \) nor \( 107 \) are perfect squares).
- So \( \sqrt{321} \) remains as \( \sqrt{321} \).
-
Simplifying \( \sqrt{721} \):
- \( 721 = 7 \times 103 \) (neither \( 7 \) nor \( 103 \) are perfect squares).
- So \( \sqrt{721} \) remains as \( \sqrt{721} \).
Since neither square root simplifies nicely to a simpler form, we can state:
\[ \sqrt{321} + \sqrt{721} \]
However, we can add them underneath a common square root if applicable:
\[ \sqrt{321} + \sqrt{721} = \sqrt{321 + 721} \]
Calculating \( 321 + 721 = 1042 \), we have:
\[ \sqrt{321} + \sqrt{721} = \sqrt{1042} \]
Now, we should check if \( \sqrt{1042} \) can be simplified:
- \( 1042 = 2 \times 521 \), and since \( 521 \) is not a perfect square, we keep it as \( \sqrt{1042} \).
Thus, we find that:
- The most simplified answer based on your provided options would be \( \sqrt{1042} \).
Therefore, the correct response is:
1042−−√ \( 10 \sqrt{42} \) is after calculating \( \sqrt{1042} = \sqrt{2 \times 521} \).
So:
\[ 10 \sqrt{42} \text{ gives us the approximate way to present this answer.} \]
The final answer depends on the way the simplification went: we confirm it's \( \sqrt{1042} \) or \( 10\sqrt{42} \).
Thus,
- The answer is \( \sqrt{1042} \).