Look for the largest square factor of 343. Since 343 = 49 × 7 and √49 = 7, we get √343 = 7√7. To simplify a surd, split the number under the root into a perfect-square factor and the remaining factor. Take the square root of the perfect square outside the radical. The expression is simplified when no square factor greater than 1 remains under the root. The correct answer is 7√7, which matches the calculation or reasoning shown.