1. The problem is to understand what surds are and how to simplify them. 2. A surd is an irrational root that cannot be simplified to remove the root. For example, $\sqrt{2}$ is a surd because it cannot be simplified to a rational number. 3. The general rule for simplifying surds is to factor the number inside the root into its prime factors and take out pairs (for square roots) or groups corresponding to the root's degree. 4. For example, to simplify $\sqrt{50}$: $$\sqrt{50} = \sqrt{25 \times 2}$$ 5. Since $25$ is a perfect square, we can take it out of the root: $$\sqrt{50} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$$ 6. This is the simplified form of the surd. 7. Remember, you cannot simplify surds if the number inside the root does not have a perfect square factor. 8. Another example: $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$. 9. This method applies to cube roots and other roots as well, by taking out perfect cubes, fourth powers, etc. 10. To summarize, surds are irrational roots, and simplifying them involves factoring and extracting perfect powers from under the root. Final answer: Surds are irrational roots like $\sqrt{2}$, and they can be simplified by factoring the radicand and extracting perfect powers, e.g., $\sqrt{50} = 5\sqrt{2}$.