Section 5.1: Properties of Radicals
This section introduces the basic properties of radicals, including simplifying, multiplying, and dividing radical expressions.
Example 1: Simplifying a Radical
Simplify \( \sqrt{50} \).
Step 1: Factor 50: \( 50 = 25 \cdot 2 \)
Step 2: Split the radical: \( \sqrt{50} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \)
Example 2: Multiplying Radicals
Compute \( \sqrt{3} \cdot \sqrt{12} \).
Step 1: Multiply under one radical: \( \sqrt{3 \cdot 12} = \sqrt{36} \)
Step 2: Simplify: \( \sqrt{36} = 6 \)
Practice Problems
- Simplify \( \sqrt{72} \)
- Simplify \( \sqrt[3]{16} \)
- Multiply \( \sqrt{2} \cdot \sqrt{8} \)
- Divide \( \sqrt{50} / \sqrt{2} \)
- Simplify \( \sqrt{18} + \sqrt{8} \)