Lesson 52: Introduction to Square Roots and Radicals
A radical is an expression that includes a square root, cube root, or higher root. The most common radical is the square root, denoted by the symbol √. Understanding radicals is essential for simplifying expressions and solving equations.
Key Definitions
- Square Root: The number which, when squared, gives the original number. Example: √9 = 3.
- Radicand: The number inside the radical symbol. Example: in √16, 16 is the radicand.
- Index: The small number that indicates the root type. For square roots, the index is 2 (usually omitted). Example: ∛8 = 2 is a cube root.
Examples
Example 1: √25 = 5 because 5² = 25
Example 2: √36 = 6 because 6² = 36
Example 3: ∛27 = 3 because 3³ = 27
Example 4: √0 = 0, √1 = 1
Practice Problems
- Find the square root: √49
- Find the square root: √64
- Find the cube root: ∛125
- Find the square root: √100
- Find the cube root: ∛8