CP Algebra 2
nth Root:
6.1 notes: Roots and Radical Expressions
For any real numbers a and b, and any positive integer n, if a n = b, then a is an nth root of b
Examples:
Possible REAL ROOTS of a REAL NUMBER:
Type of Number
Number of Real nth Roots________Number of Real nth Roots
(n is even)
(n is odd)
Positive
2
1
Negative
none
1
Example: Finding all real roots
a. the cube roots of 0.008, -1000 and 1/27
b. the fourth roots of 1, -0.0001 and 16/81
Radicand: number under the radical sign
Index: Degree of the Root
Principal Root: the positive root when a number has two real roots
Find each real number root
a.
3
8
b.
 100
c.
3
 27
d.
4
81
e.
3
 27c 6
Example: Simplify each radical expression
a.
4x 6
b.
3
a 3b 6
c.
4
x4 y8
d.
4x 2 y 4