1. The problem is to simplify the expression $\sqrt{75}$.\n2. Begin by factoring 75 into its prime factors: $75 = 25 \times 3$.\n3. Since $25 = 5^2$, we can rewrite $\sqrt{75}$ as $\sqrt{25 \times 3}$.\n4. Use the property of square roots that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ to get $\sqrt{25} \times \sqrt{3}$.\n5. Calculate $\sqrt{25} = 5$, so the expression simplifies to $5 \sqrt{3}$.\n6. Therefore, the simplified form of $\sqrt{75}$ is $5 \sqrt{3}$.