Look for the largest square factor of 63. Since 63 = 9 × 7 and √9 = 3, we get √63 = 3√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 3√7, which matches the calculation or reasoning shown.