Radicals. 37 



5. The 71 th root of the product of several quantities is equal to the 

 product of the n th roots of the several quantities. 



That is, VabFT'.=Va V~b V'c . . 



1 A i_ J: 



or (a b c . .)"=^a"b"c" . . 



6. The 71 th root of the quotient of tzvo numbers is equal to the 

 quotie7it of their 71 th 7'oots. 



That is. _, ^ „ 



\_ 1 

 f^ ) " a 

 or 



n \a_ya 



\aY _a- 

 \b] - \L 



7. The nrth 7vot of a qua7itity equals the 11 th 7'oot of the rth 

 root of the qua7itity. 



That is, 'V~a=.V'\ra. 



1 



(ay-=\(ay\ 



or 



8. To REMOVE A Factor from beneath the Radical 

 Sign. When any factor of the quantity beneath the radical sign 

 is an exact power of the indicated root, the root of that factor may 

 be taken and written as a coefficient while the other factors are 



left beneath the radical sign. Thus n^i28 may be written v/64 X 2, 

 which, by Art. 5, equals V/64X ^2, which equals 8^/2. As an- 

 other case take ^^^i^ax', which equals ^^%x^ X 2ax= ^Sji'^ X '^2ax 

 = 2 x^^2ax. It is readily seen that this same process may be ap- 

 plied to any similar case. 



9. Examples. Remove as many factors as possible from be- 

 neath the radical signs in the following : 



>/8io. 

 ^^8To. 



v^'^JSoS. 



