Beginning Algebra, 11th Edition

530 CHAPTER 8 Roots and Radicals

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   5. 
      
      
      
      6. 
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   8. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   


4. 
   
   
   
   11. 
       
       
       
       12. 
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   14. 
       
       
       
       15. 
           
       
       
       
       
   
   
   
   


6. 
   
   
   
   17. 
       
       
       
       18. 
           
       
       
       
       
   
   
   
   


7. 
   
   
   
   20. 
       
       
       
       21. 
           
       
       
       
       
   
   
   
   


8. 
   
   
   
   23. 
       
   
   
   
   


9. 
   
   
   
   25. 
       
   
   
   
   

Students often have trouble distinguishing between the following two types of problems:

2316 t^2 - 2354 t^2 + 23128 t^2 A 1 + 233 BA 1 - 233 + 239 B

A^2107 -^2106 BA^2107 +^2106 B x^24 x^5 -^324 x^9 +x^224 x

B

3

16

81

275 x- 212 x A 5 + 323 B^2

26 - 25

26 + 25

• 4
  234

8250

2225

623

B 5212

2

3 x

5

26 - 1

12

239

238 x^3 y^5 z^6

1

2 t + 23

A^23 +^6 BA^23 -^6 B

8

27 - 25

1 + 22

1 - 22

3

26

A^325 -^227 B

298 - 272 + 250 2

5210 - 8210 25 A 25 - 23 B A 1 + 23 BA 2 - 26 B

SUMMARY EXERCISESon Operations with Radicals

Simplifying a Radical Involving

a Square Root

Exercise: Simplify

Answer: 5

In this situation, represents the posi-

tive square root of 25, namely, 5.

Solving an Equation by Using

Square Roots

Exercise: Solve

Answer:

In this situation, has either of two

solutions: the negative square root of 25 or

the positive square root of 25—that is,

or 5. (See Exercise 36.)

• 5

x^2 = 25

5 - 5, 5 6

x^2 =25.

225

225.

Use the preceding information to work Exercises 26–35.

26. (a)Simplify
    (b)Solve
    27. (a) Simplify
    (b)Solve x^2 =81.

281.

x^2 =36.

236.

28. (a)Solve
    (b)Simplify
    29. (a) Solve
    (b)Simplify - 29.

x^2 =9.

• 
  
  
  
  24. 
      
  
  
  
  

x^2 =4.

30. (a)Solve
    (b)Simplify
    31. (a) Solve
    (b)Simplify 2491.

x^2 = 491.

2

1

4.

x^2 =^14.

32. (a)Simplify
    (b)Solve
    33. (a) Simplify
    (b)Solve x^2 = 10049.
    
    
    • 
      
      
      
      210049. x^2 =^1625.
      
      
      
      
    
    
    
    

• 
  
  
  
  21625. 
         
  
  
  
  

34. (a)Solve
    (b)Simplify
    35. (a) Solve
    (b)Simplify 2 0.16.

x^2 =0.16.

2 0.04.

x^2 =0.04.

36.Use the zero-factor property (Section 6.5)to show that the solution set of is

5 - 5, 5 6.

x^2 = 25

Perform all indicated operations and express each answer in simplest form. Assume that all

variables represent positive numbers.

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