1. **State the problem:** Simplify the square roots $\sqrt{12}$, $\sqrt{27}$, and $\sqrt{50}$.\n\n2. **Formula and rules:** To simplify a square root, find the largest perfect square factor of the number inside the root and use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$.\n\n3. **Simplify $\sqrt{12}$:**\n$12 = 4 \times 3$ where 4 is a perfect square.\n$$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}.$$\n\n4. **Simplify $\sqrt{27}$:**\n$27 = 9 \times 3$ where 9 is a perfect square.\n$$\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}.$$\n\n5. **Simplify $\sqrt{50}$:**\n$50 = 25 \times 2$ where 25 is a perfect square.\n$$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}.$$\n\n**Final answers:**\n- $\sqrt{12} = 2\sqrt{3}$\n- $\sqrt{27} = 3\sqrt{3}$\n- $\sqrt{50} = 5\sqrt{2}$