To simplify the expression \(32\sqrt{} - 43\sqrt{} + 62\sqrt{} + 3\sqrt{}\), we should first rewrite it clearly:
\[ 3\sqrt{2} - 4\sqrt{3} + 6\sqrt{2} + 3\sqrt{1} \]
Notice that \(3\sqrt{1} = 3\), and it can also represent as \(3\). So the expression can be rearranged as follows:
Combine like terms for \( \sqrt{2} \):
\[ (3\sqrt{2} + 6\sqrt{2}) + (-4\sqrt{3}) + 3 \] \[ = 9\sqrt{2} - 4\sqrt{3} + 3 \]
So the total result simplifies to:
\[ 9\sqrt{2} - 4\sqrt{3} + 3 \]
Now let's check your responses for a match:
None of the provided responses directly match this result.
However, among the possible answers provided, it appears:
- \(-3\sqrt{2} + 5\sqrt{3}\)
- \(9\sqrt{4} - 4\sqrt{6}\)
- \(9\sqrt{2} - 3\sqrt{3}\)
- \(6\sqrt{10}\)
The closest simplification we achieved mathematically was \(9\sqrt{2} - 4\sqrt{3} + 3\), which wasn't in the exact options you provided.
If you would like a reassessment or new examination based on provided options, please clarify!