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3\times 48\sqrt{6}
Factor 13824=48^{2}\times 6. Rewrite the square root of the product \sqrt{48^{2}\times 6} as the product of square roots \sqrt{48^{2}}\sqrt{6}. Take the square root of 48^{2}.
144\sqrt{6}
Multiply 3 and 48 to get 144.