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6\times 8\sqrt{2}-4\sqrt{200}+2\sqrt{9}
Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.
48\sqrt{2}-4\sqrt{200}+2\sqrt{9}
Multiply 6 and 8 to get 48.
48\sqrt{2}-4\times 10\sqrt{2}+2\sqrt{9}
Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.
48\sqrt{2}-40\sqrt{2}+2\sqrt{9}
Multiply -4 and 10 to get -40.
8\sqrt{2}+2\sqrt{9}
Combine 48\sqrt{2} and -40\sqrt{2} to get 8\sqrt{2}.
8\sqrt{2}+2\times 3
Calculate the square root of 9 and get 3.
8\sqrt{2}+6
Multiply 2 and 3 to get 6.