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7\times 7\sqrt{7}
Factor 343=7^{2}\times 7. Rewrite the square root of the product \sqrt{7^{2}\times 7} as the product of square roots \sqrt{7^{2}}\sqrt{7}. Take the square root of 7^{2}.
49\sqrt{7}
Multiply 7 and 7 to get 49.