Sec. P.2 Cont.

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

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

Ex. 6 √36 -√36 5√-32 d) e) 4√-81

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

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

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