1. Let's start by understanding what radicals are. A radical expression involves roots, such as square roots ($\sqrt{x}$), cube roots ($\sqrt[3]{x}$), etc. 2. The most common radical is the square root. The square root of a number $a$ is a number $b$ such that $b^2 = a$. 3. Important rules for radicals: - $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$ - $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ - $\sqrt{a^2} = |a|$ 4. Simplifying radicals means expressing them in simplest form. For example, $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$. 5. Rationalizing the denominator means eliminating radicals from the denominator. For example, $\frac{1}{\sqrt{3}}$ can be rationalized by multiplying numerator and denominator by $\sqrt{3}$: $$\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{3}}{3}$$ 6. Practice problem: Simplify $\frac{\sqrt{18}}{\sqrt{2}}$. Step 1: Use the quotient rule for radicals: $$\frac{\sqrt{18}}{\sqrt{2}} = \sqrt{\frac{18}{2}}$$ Step 2: Simplify inside the radical: $$\sqrt{\frac{18}{2}} = \sqrt{9}$$ Step 3: Calculate the square root: $$\sqrt{9} = 3$$ Final answer: $3$. This is how you simplify radicals and rationalize denominators. Keep practicing these steps to prepare for your test!