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\left(10\sqrt{6}+\sqrt{6}-\sqrt{24}\right)\sqrt{6}
Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.
\left(11\sqrt{6}-\sqrt{24}\right)\sqrt{6}
Combine 10\sqrt{6} and \sqrt{6} to get 11\sqrt{6}.
\left(11\sqrt{6}-2\sqrt{6}\right)\sqrt{6}
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}.
9\sqrt{6}\sqrt{6}
Combine 11\sqrt{6} and -2\sqrt{6} to get 9\sqrt{6}.
9\times 6
Multiply \sqrt{6} and \sqrt{6} to get 6.
54
Multiply 9 and 6 to get 54.