1. Sec. P.2 Cont.

2. Radicals and their properties
Square Root
Opposite of squaring
One of its two equal factors
√25
Cube Root
Opposite of cubing
One of its three equal factors

3. Complete the chart n n2 n3 n4 n5 -3 9
-27 -2 4 -1 1 2 3

4. Ex. 6
√36
-√36
5√-32 d)
e) 4√-81

5. Generalizations for n√a
a is positive real # and n is positive even integer – 2 real roots – a positive and negative
Ex. 4√16
a is any real # and n is an odd integer – 1 real root
Ex. 3√27 or 3√-27
a is a negative real # and n is even – no real roots
√-4 (imaginary)
n√0 = 0

6. Perfect Square Numbers
Integers that have integer square roots
1, 4, 9, 16, 25, 36, …
Perfect Cubes
Numbers that have integer cube roots
1, 8, 27, 64, 125, …
Properties p. 20
Pay attention to #6

7. Simplest Form
All possible factors have been removed from the radical. (No factor of the # can be “pulled out”)
No radicals in the denominator. (The process of getting them out is called rationalizing the denominator.)
Index of radical is reduced