1. **State the problem:** Simplify the square root expression $\sqrt{387}$. 2. **Recall the formula and rules:** To simplify a square root, find the largest perfect square factor of the number under the root. Use the property $\sqrt{a \cdot b} = \sqrt{a} \times \sqrt{b}$. 3. **Factor 387:** $$387 = 3 \times 129 = 3 \times 3 \times 43 = 9 \times 43$$ 4. **Apply the square root property:** $$\sqrt{387} = \sqrt{9 \times 43} = \sqrt{9} \times \sqrt{43}$$ 5. **Simplify the square root of the perfect square:** $$\sqrt{9} = 3$$ 6. **Write the simplified form:** $$\sqrt{387} = 3 \times \sqrt{43}$$ 7. **Final answer:** $$\boxed{3\sqrt{43}}$$