1. The term "surd" refers to irrational numbers expressed in root form, such as square roots that cannot be simplified to rational numbers. 2. For example, $\sqrt{2}$ is a surd because it is an irrational number. 3. To simplify a surd, factorize under the root into prime factors and extract perfect squares. 4. For example, simplify $\sqrt{50}$: - Factorize 50: $50 = 25 \times 2$ - Write $\sqrt{50}$ as $\sqrt{25 \times 2}$ - Use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, so $\sqrt{50} = \sqrt{25} \times \sqrt{2}$ - Simplify $\sqrt{25}$ to 5, so $\sqrt{50} = 5\sqrt{2}$ 5. This is the simplest surd form since $\sqrt{2}$ cannot be simplified further.