Radicals. 39 



II. Examples. Integralize the expressions under the' radicla 

 signs in the following, simplifying the result in each case by Art. 

 8, if necessary : 



Process: 5 |.-A_=r f ^ _ I 6 ^ .^^. 

 \fi47 ^>i49X3 N49X9 ^' 



2. 



^u- 



4- ^''l 



J 





9- 



10. 





4/ 



12. To LOWER THE Index OF A RADICAL. It is plain that 

 t^25 by Art. 7 = V^ ^^ = v/ 5 ; also that V ^a^=\^^^~2=:\/2a; 



similarly v/4(^^= v^ ^ .^2=\V2(^ ; and in general, "-v/^"=Vv'^= 



V^ . From this we see that the index of a radical can be lowered 

 if the expression under the radical is a perfect power correspond- 

 ing to some factor of the original index. 



13. Examples. Reduce the following to their simplest fomis. 

 See Art. 4. 



I. v^36x^j/^. 



6/ 2 



1000 



4- .: ^., 



5- 



