Look for the largest square factor of 117. Since 117 = 9 × 13 and √9 = 3, we get √117 = 3√13. 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 3√13, which matches the calculation or reasoning shown.