1. 7-1 R OOTS AND R ADICAL E XPRESSIONS Finding roots and simplifying radical expressions

2. F INDING ROOTS Definitions: Radicand - number under the radical sign Index – the degree of the root Even index yields both a positive and a negative root Odd index yields a root with the same sign as the radicand Principal root - with even index only – is the positive root

3. F INDING THE ROOTS Even roots Index numbers are even numbers Radicands can not be negative Negative radicands yield imaginary roots Odd roots Index numbers are odd numbers Radicands can be negative or positive Negative radicands yield negative roots Positive radicands yield positive roots Root – the opposite of a power a number that when multiplied by itself the number of times in the index yields the radicand

4. S IMPLIFYING RADICAL EXPRESSIONS Simplify the root of the coefficient Find the root of the coefficient if possible Divide the exponent of the variable by the index The answer becomes the number of the exponent of the variable outside of the radical sign The remainder is the exponent of the variable inside of the radical sign (the radicand)