1. The problem is to simplify the square root expression $\sqrt{75}$.\n\n2. Factorize 75 into its prime factors: $75 = 25 \times 3 = 5^2 \times 3$.\n\n3. Use the property of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. Thus, $\sqrt{75} = \sqrt{5^2 \times 3} = \sqrt{5^2} \times \sqrt{3}$.\n\n4. Simplify the square root of the perfect square: $\sqrt{5^2} = 5$.\n\n5. Therefore, $\sqrt{75} = 5 \sqrt{3}$. This is the simplified form.