Beginning Algebra, 11th Edition

(d)

Factor.

Multiply.

=m 234 Subtract like radicals. NOW TRY

= 4 m 234 - 3 m 234

= 2 # 2 m 234 - 3 m 234 238 m^3 = 2 m; 2327 m^3 = 3 m

= 2238 m^3 # 4 - 2327 m^3 # 4

22332 m^3 - 23108 m^3

SECTION 8.3 Adding and Subtracting Radicals 515

CAUTION A sum or difference of radicals can be simplified only if the radi-

cals are like radicals.

= 425 223 + 5233

25 + 325 Add like 25 + 523

radicals.

Unlike radicals

cannot be simplified.

Complete solution available
on the Video Resources on DVD

8.3 EXERCISES

Concept Check Fill in each blank with the correct response.

1.Simplifying the expression as , is an application of

the property.

2.The radicals and are examples of like radicals because both radicals

have the same root index, , and the same radicand,.

3. cannot be simplified because the are different.


4. cannot be simplified because the are different.

Add or subtract wherever possible. See Examples 1, 2, and 3(a).

5. 
   
   
   
   6. 
      
      
      
      7. 
         
      
      
      
      
   
   
   
   


6. 
   
   
   
   9. 
      
      
      
      10. 
          
      
      
      
      
   
   
   
   


7. 
   
   
   
   12. 
       
       
       
       13. 
           
       
       
       
       
   
   
   
   


8. 
   
   
   
   15. 
       
       
       
       16. 
           
       
       
       
       
   
   
   
   


9. 
   
   
   
   18. 
       
       
       
       19. 
           
       
       
       
       
   
   
   
   


10. 
    
    
    
    21. 
        
        
        
        22. 
            
        
        
        
        
    
    
    
    


11. 
    
    
    
    24. 
        
    
    
    
    


12. 
    
    
    
    26. 
        
    
    
    
    


13. 
    
    
    
    28. 
        
    
    
    
    


14. 
    
    
    
    30. 
        
    
    
    
    


15. 
    
    
    
    32. 
        
    
    
    
    


16. 
    
    
    
    34. 
        
    
    
    
    


17. 42316 - 32354 36. 323250 - 423128

26 # 22 + 323 215 # 23 + 225

23 # 27 + 2221 213 # 22 + 3226

5

8

2128 -

3

4

2160

3

5

275 -

2

3

245

2

3

227 +

3

4

248

1

4

2288 +

1

6

272

5272 - 3248 - 42128 4250 - 3212 - 52200

9224 - 2254 + 3220 228 - 5232 + 2248

6218 - 4232 527 - 2228 + 6263 3211 - 3299 + 5244

2275 - 212 2227 - 2300 2250 - 5272

322 + 250 26 + 27 214 + 217

217 + 2217 219 + 3219 523 + 212

622 - 822 26 + 26 211 + 211

223 + 523 625 + 825 427 - 927

4232 + 322

22 - 223

243 xy^3 - 6243 xy^3

522 + 622 15 + 6222 , or 11 22

NOW TRY
EXERCISE 3
Simplify. Assume that all
variables represent nonnega-
tive real numbers.

(a)

(b)

(c)

(d)

NOW TRY ANSWERS

3. (a) (b)
   (c)- 2 k^223 (d) 14 y 232 y^2

1222 926 x

23128 y^5 + 5 y 2316 y^2

5 k^2212 - 4227 k^4

2150 x+ 2224 x

27 # 214 + 522