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Real Numbers

Radicals

Basic Algebra & Polynomials

Linear Equations

Inequalities & Absolute Value

Rational Expressions 1

Rat'l. Exp. 2 - mult&div

Rat'l. Exp. 3 - add&subt

Exponents

Slope & Equations of Lines

Review&Test

 

 

jdsmathnotes

 


 

 UNIT 1  : ALGEBRA PREP

 LESSON 1:  REAL NUMBERS - RADICALS

 

Examples Of Radicals:

 

 

NOTE:  Each of these examples is an irrational real number.

 

 Properties of Radicals:

 

Text Box: 	          
 
                       

 

 

 

 

 

 

 

Example 1:

 

Mixed and Entire Radicals:

 

Example 2:  Write as mixed radicals.

                                                                                                                              

 

Solutions:

                                                           

 

 

 

 

                                                           

 

Text Box: Tips for Changing to Mixed Radicals:
·	Break the radical into two factors
·	Use the following set of perfect squares to get the first factor 
·	{4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, …}
·	Take the square root of the first number to get the first factor of the mixed radical.
 


                       

 

 

 

 

 

 

 

 

Example 3:  Write as entire radicals.

                                                                                                       

 

Solutions:

 

                                                  

 

 

                                               

 

Multiplying Radicals:

Example 4:  Simplify

                                                                                     

 

 

 

Solutions:

 

                                               

 

 

 

Addition and Subtraction of Radicals:

Radicals are added/subtracted just as in ordinary algebra using LIKE TERMS.

Examples:

                    2x – 3y + 5x – 6y = 2x + 5x – 3y – 6y = 7x – 9y

Similarly    

 

Example 5:  Simplify

                                                

Solutions:

 

 

Example 6:  Simplify

                                            

 

Solutions:

Again we follow the rules of ordinary algebra for expanding

 

Recall from ordinary algebra the product of two binomials:

           

            (x + 3)(x + 5) = x(x + 5) + 3(x + 5)

                                  = x2 + 5x + 3x + 15

                                  = x2 + 8x + 15

 

 

 

 

Division of Radicals:

 

Recall all of the properties of radicals mentioned above:

 

Text Box: 	          
  
                       

                       

 

 

 

 

 

 

 

 

Example 7:  Simplify

 

Division of Radicals with Irrational denominators:  Examples: 

 

These are simplified by a process called rationalizing the denominator.

 

Example 8:  Simplify by rationalizing the denominator.

 

Example 9:  Simplify

Example 10: Simplify

Example 11: Simplify


 

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