Evaluate
16\sqrt{6}+20\sqrt{2}+12\approx 79.476107132
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12+12\sqrt{2}+8\sqrt{2}+8\sqrt{12}\sqrt{2}
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}.
12+20\sqrt{2}+8\sqrt{12}\sqrt{2}
Combine 12\sqrt{2} and 8\sqrt{2} to get 20\sqrt{2}.
12+20\sqrt{2}+8\sqrt{2}\sqrt{6}\sqrt{2}
Factor 12=2\times 6. Rewrite the square root of the product \sqrt{2\times 6} as the product of square roots \sqrt{2}\sqrt{6}.
12+20\sqrt{2}+8\times 2\sqrt{6}
Multiply \sqrt{2} and \sqrt{2} to get 2.
12+20\sqrt{2}+16\sqrt{6}
Multiply 8 and 2 to get 16.
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