1. Roots and Radical Expressions

2. Roots
Nth roots
If an=b then a is an nth root of b
For any real numbers a, b and any positive integer n
Ex: Since 24=16 and (-2)4=16, both 2 and -2 are roots of 16
Ex: x4=-16
Since there is no REAL number x, then the above has no real fourth root

3. Number of Real Roots Type of number
Number of real nth roots when n is EVEN
Number of real nth roots when n is ODD
Positive 2 1
Negative
none

4. Finding All Real Roots Evaluate the roots of all numbers given
Ex 1: Cube root of .008, -1000, and 1/27 /3
Ex 2: Fifth roots of 0, -1, 32

5. Radicals Radical sign Terminology radicand n Index
When a number has two real roots, the positive root is call the principal root
Index
- gives the degree of the root

6. Examples! 