Intermediate Algebra (11th edition)

= 282 Leave in radical form. NOW TRY

= 292 + 1 - 122

= 236 - 1 - 3242 + 14 - 522 x 2 =6,y 2 =4,x 1 =3,y 1 = 5

d= 21 x 2 - x 122 + 1 y 2 - y 122

450 CHAPTER 8 Roots, Radicals, and Root Functions

Substitute carefully.

NOW TRY
EXERCISE 9
Find the distance between the
points and 1 - 4, - 32 1 - 8, 6 2.

Complete solution available
on the Video Resources on DVD

8.3 EXERCISES

Multiply, if possible, using the product rule. Assume that all variables represent positive real

numbers. See Examples 1 and 2.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   6. 
      
      
      
      7. 
         
         
         
         8. 
            
         
         
         
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   10. 
       
       
       
       11. 
           
           
           
           12. 
               
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   14. 
       
       
       
       15. 
           
           
           
           16. 
               
           
           
           
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   18. 
       
       
       
       19. 
           
           
           
           20. 
               
           
           
           
           
       
       
       
       
   
   
   
   

Simplify each radical. Assume that all variables represent positive real numbers. See Example 3.

21. 22. 23. 24.

25. 26. 27. 28.

29. 30. 31. 32.

33. 34. 35. 36.

Express each radical in simplified form. See Example 4.

37. 
    
    
    
    38. 
        
        
        
        39. 
            
            
            
            40. 
                
                
                
                41. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


38. 
    
    
    
    43. 
        
        
        
        44. 
            
            
            
            45. 
                
                
                
                46. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


39. 
    
    
    
    48. 
        
        
        
        49. 
            
            
            
            50. 
                
                
                
                51. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


40. 
    
    
    
    53. 
        
        
        
        54. 
            
            
            
            55. 
                
                
                
                56. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


41. 
    
    
    
    58. 
        
        
        
        59. 
            
            
            
            60. 
                
            
            
            
            
        
        
        
        
    
    
    
    

61.A student claimed that is not in simplified form, since , and 8 is a

perfect cube. Was his reasoning correct? Why or why not?

62.Explain in your own words why 23 k^4 is not a simplified radical.

2314 14 = 8 + 6

- 25486 - 252048 26128 261458

23375 - 24512 - 241250 2564 25128

23128 2324 23 - 16 23 - 250 2340

- 248 - 228 - 224 230 246

212 218 2288 272 - 232

B

5

32

B y^20

5

1

x^15

-

B

4

625

y^4

-

B

4

81

x^4

B

3

t

B^125

3

r^2

B^8

3 -

216

B^125

3 -

27

64

B

w^10

B^36

p^6

B^81

k

B^100

x

25

B

13

B^49

3

B^25

16

B^49

64

121

242 x# 243 x^2243 y^2 # 246 y 237 # 243 258 # 2612

237 x# 232 y 239 x# 234 y 2411 # 243 246 # 249

214 # 23 pqr 27 # 25 xt 232 # 235 233 # 236

25 # 26 210 # 23 214 # 2 x 223 # 2 t

23 # 23 25 # 25 218 # 22 212 # 23

Using the Distance Formula

Find the distance between the points and

Designating the points as and is arbitrary. We choose

1 - 3, 5 2 and 1 x 2 , y 22 = 1 6, 4 2.

1 x 1 , y 12 1 x 2 , y 22 1 x 1 , y 12 =

1 - 3, 5 2 1 6, 4 2.

EXAMPLE 9

NOW TRY ANSWER

9. 297