1. Chapter 10 Exponents & Radicals Phong Chau

2. Section 10.1 Radical Expressions & Functions

3. Definition Q: What number when squared equals 36? A: 6 Q: Is it the only answer? A: No  6 is called a square root of 36  -6 is also a square root of 36 Def: b is called a square root of the number a if b 2 =a.

4. Examples  A square root of 36 is 6  Another square root of 36 is -6  A square root of 121 is 11  Another square root of 121 is -11  A square root of 0 is 0  A square root of -4 is Remarks: 1)Each positive number has two square roots: a positive square root and a negative square root 2)0 has a unique square root 3)Each negative number has no square root. NONE

5. Notation The positive square root of a number a is denoted by the radical symbol: It’s also called the principal square root of a. Examples:

6. Definition Def: b is called an n th root of the number a if b n =a. The principal n th root of a is denoted by index of the radical radical symbol radicand Q: What number when cubed equals 8? A: 2 Q: What number when raised to the fifth power equals -32? A: -2 because

7. Examples No such real number exists

8. Examples Evaluate the following radical expressions

9. Examples Evaluate the following radical expressions When the index is odd When the index is even

10. Examples Simplify the expressions When n is odd When n is even

11. Radical Functions Graph the following functions Find the domain of the following functions