1. **State the problem:** Simplify the surds (square roots) of the numbers 12, 28, 32, 125, 300, 72, and 20. 2. **Formula and rules:** To simplify a surd $\sqrt{n}$, find the largest perfect square factor of $n$ and use the property: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ where $a$ is the perfect square. 3. **Simplify each surd:** - $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$ - $\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}$ - $\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$ - $\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}$ - $\sqrt{300} = \sqrt{100 \times 3} = 10\sqrt{3}$ - $\sqrt{72} = \sqrt{36 \times 2} = 6\sqrt{2}$ - $\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$ 4. **Final answers:** $$\sqrt{12} = 2\sqrt{3}, \quad \sqrt{28} = 2\sqrt{7}, \quad \sqrt{32} = 4\sqrt{2}, \quad \sqrt{125} = 5\sqrt{5}, \quad \sqrt{300} = 10\sqrt{3}, \quad \sqrt{72} = 6\sqrt{2}, \quad \sqrt{20} = 2\sqrt{5}$$