To evaluate \( 1224 \sqrt{3300} \), we first simplify \( \sqrt{3300} \).
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Factor \( 3300 \): \[ 3300 = 33 \times 100 = 33 \times 10^2 \] \[ 33 = 3 \times 11 \quad \text{and} \quad 100 = 10^2 = (10)^2 \] Thus, we can write: \[ 3300 = 3 \times 11 \times 100 = 3 \times 11 \times 10^2 \]
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Taking the square root: \[ \sqrt{3300} = \sqrt{3 \times 11 \times 100} = \sqrt{3 \times 11} \times \sqrt{100} = 10 \sqrt{33} \]
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Substitute back into the expression: \[ 1224 \sqrt{3300} = 1224 \times 10 \sqrt{33} \] \[ = 12240 \sqrt{33} \]
Thus, the value of \( 1224 \sqrt{3300} \) simplifies to: \[ \boxed{12240 \sqrt{33}} \]