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6\times 2\sqrt{2}-4\times 8\sqrt{12}+3\sqrt{18}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
12\sqrt{2}-4\times 8\sqrt{12}+3\sqrt{18}
Multiply 6 and 2 to get 12.
12\sqrt{2}-32\sqrt{12}+3\sqrt{18}
Multiply 4 and 8 to get 32.
12\sqrt{2}-32\times 2\sqrt{3}+3\sqrt{18}
Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.
12\sqrt{2}-64\sqrt{3}+3\sqrt{18}
Multiply 32 and 2 to get 64.
12\sqrt{2}-64\sqrt{3}+3\times 3\sqrt{2}
Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.
12\sqrt{2}-64\sqrt{3}+9\sqrt{2}
Multiply 3 and 3 to get 9.
21\sqrt{2}-64\sqrt{3}
Combine 12\sqrt{2} and 9\sqrt{2} to get 21\sqrt{2}.