To simplify the expression \( 3\sqrt{21} + 7\sqrt{12} \), we first simplify \( \sqrt{12} \).
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We can express \( \sqrt{12} \) as: \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}. \]
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Now replace \( \sqrt{12} \) in the original expression: \[ 7\sqrt{12} = 7 \cdot 2\sqrt{3} = 14\sqrt{3}. \]
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Therefore, the expression becomes: \[ 3\sqrt{21} + 14\sqrt{3}. \]
Since \( \sqrt{21} \) and \( \sqrt{3} \) are both irrationals that cannot be simplified further and do not share a common radical term, the expression \( 3\sqrt{21} + 14\sqrt{3} \) is already in its simplest form.
Thus, the final answer is: \[ 3\sqrt{21} + 14\sqrt{3}. \]
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