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7\times 16\sqrt{2}
Factor 512=16^{2}\times 2. Rewrite the square root of the product \sqrt{16^{2}\times 2} as the product of square roots \sqrt{16^{2}}\sqrt{2}. Take the square root of 16^{2}.
112\sqrt{2}
Multiply 7 and 16 to get 112.