Freeman Chapter 12

1. 12.6 - Radical Equations

1.1. 1. Factor 2. Isolate radical 3. Square both sides 4. Finish solving 5. Check for even root answer

1.2. Eliminate radicals, when: Addition - FOIL Radical - Cancel Multiply - Square

2. 12.5 - Multiplying

2.1. Simplification Use foil system to simplify Eye for conjugates, middle terms drop out

2.2. Rationalize the Denominator *Factor First! 1. Remove radical in denominator 2. Multiple to make denominator 1

3. 12.7 - Imaginary Numbers

3.1. Solve problems as usual, only replacing imaginary number with their equivalent

3.2. i^-3 = i i^-2 = -1 i^-1 = -i i^0 = 1 i = i i^2 = -1 i^3 = -i i^4 = 1 i^5 = i

4. 12.1 - Radical Expressions

4.1. Even Index - can only = + #'s, when -- use | | Odd Index - can be -- outcome Even index, odd radicand - not real *Use | | and check to rid

5. 12.2 - Rational Exponents

5.1. Fractional notation to Radical notation, vice versa -denominator is index and numerator is power Simplify *1/2 power is root

6. 12.3 - Simplifying and Multiplying Radicals

6.1. 1. Check for factors, factor complete 2. Prime factor 3. Rewrite 4. Pull out perfects

7. 12.4 - Rationals

7.1. Adding and Subtracting 1. Factor Completely 2. Add like terms * Do not change the thing you are adding, change how many things you have

7.2. Dividing Rationals 1. Simplify by dividing rationals in fraction 2. Simplify across * No fractions in radicals, no radicals in denominator