Understanding Roots and Radicals in Mathematics

1. Chapter 8 – Roots, Radicals and Rational Functions Chapter 8-1: Radical Expressions and Graphs

2. Chapter 8 – No Calculators

3. Terminology “The cube root of eight”  If the index is 2, it is called a square root If the index is 3, it is called a cuberoot If the index is 4, it is called a fourth root If the index is 5, it is called a fifth root and so on…

4. Roots and Exponents = 125 What do you notice? What is the relationship here?

5. nth Root Rules • If n is even and a is positive or 0, then - represents the negative nth root of a • If n is even and a is negative, then is not a real number • If n is odd, then there is exactly one real nth root of a, written

6. Find Each Root • = ____ • = ____ • _____ • _____ • _____

7. Graphing Radical Functions (By Hand) • This topic is on page 429 and 430 in the textbook and will be covered on the board in class. No notes will be provided.

8. Simplifying Square Roots by Using Absolute Value • If n is an even positive integer, then • If n is an oddpositive integer, then Examples:

9. Simplifying Higher Roots • Simplify each root: • _______ • _______ • -_______ • -_______ • = _______ • = _______