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4\sqrt{6}-2\sqrt{6}+\sqrt{59}
Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.
2\sqrt{6}+\sqrt{59}
Combine 4\sqrt{6} and -2\sqrt{6} to get 2\sqrt{6}.