To simplify the expression \( 3\sqrt{21} + 7\sqrt{12} \), we can start by simplifying \( \sqrt{12} \):
\[ \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \]
Now, we can substitute this back into the expression:
\[ 3\sqrt{21} + 7\sqrt{12} = 3\sqrt{21} + 7(2\sqrt{3}) = 3\sqrt{21} + 14\sqrt{3} \]
Now, the expression \( 3\sqrt{21} + 14\sqrt{3} \) cannot be simplified further because \( \sqrt{21} \) and \( \sqrt{3} \) do not share any common factors.
Now, looking at the responses provided:
- \( \sqrt{52} \)
- \( \sqrt{24} + \sqrt{28} \)
- \( 10\sqrt{21} \)
- \( 10\sqrt{42} \)
None of these answers match \( 3\sqrt{21} + 14\sqrt{3} \). So based on the calculations, the simplified form remains \( 3\sqrt{21} + 14\sqrt{3} \). Therefore, none of the given options are correct.