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4\sqrt{6}-3\sqrt{6}
Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.
\sqrt{6}
Combine 4\sqrt{6} and -3\sqrt{6} to get \sqrt{6}.