To simplify the expression \( 5\sqrt{48} + 9\sqrt{3} \), we start by simplifying \( \sqrt{48} \).
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Simplifying \( \sqrt{48} \): \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]
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Substituting back into the expression: \[ 5\sqrt{48} = 5(4\sqrt{3}) = 20\sqrt{3} \]
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Now replace \( 5\sqrt{48} \) in the original expression: \[ 20\sqrt{3} + 9\sqrt{3} \]
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Combining like terms: \[ (20 + 9)\sqrt{3} = 29\sqrt{3} \]
Thus, the simplified form of \( 5\sqrt{48} + 9\sqrt{3} \) is \( \boxed{29\sqrt{3}} \).