1. **State the problem:** Simplify the radical expression $\sqrt{75}$.\n\n2. **Recall the formula and rules:** To simplify a square root, find the prime factorization of the number inside the root and look for perfect squares. Use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$.\n\n3. **Prime factorization of 75:** $75 = 25 \times 3$.\n\n4. **Simplify using perfect squares:** Since $25$ is a perfect square, $\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3}$.\n\n5. **Evaluate the square root of the perfect square:** $\sqrt{25} = 5$.\n\n6. **Final simplified form:** $\sqrt{75} = 5\sqrt{3}$.\n\nThis means the simplified radical expression is $5\sqrt{3}$, which is easier to work with in further calculations.