To simplify \( 7\sqrt{99} \), we start by breaking down the square root:
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Factor \( 99 \) into its prime factors: \[ 99 = 9 \times 11 = 3^2 \times 11 \]
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Now, we can express the square root: \[ \sqrt{99} = \sqrt{9 \times 11} = \sqrt{9} \times \sqrt{11} = 3\sqrt{11} \]
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Substitute back into the expression: \[ 7\sqrt{99} = 7 \times 3\sqrt{11} = 21\sqrt{11} \]
Thus, the simplified form of \( 7\sqrt{99} \) is: \[ \boxed{21\sqrt{11}} \]
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