SURDS. 117 



PROBLEM I. 

 To reduce a rational quantity to. the form of a surd^ 



' RULE. 



Raise the quantity to a power equivalent to that,, denote 

 cd by the index of the surd ; then over this new quantity 

 place the radical sign, and it will be of the form required. 



EXAMPLES. 



1. To reduce 3 to the form of the square root. 



First 3X3=3 ^==9 j then ^/p is the answer. 



2. To reduce 2a;* to the form of the cube root. 



First, 2A?'X2A;'X2Ar'=2;^.*| zzZx^ -, 



Then s/^^^i or 8;c^l , is the answer. 



3. Reduce 5 to the form of the cube root. 



Ans. 125LS or -v/125. 



4. Reduce ~Xj to the form of the square root. 



Ans. \/\x^y''\ 



e. Reduce 2 to the form of the 5th root. , 



Ans. 3 2 p. 



PROBLEM II. 



21? reduce quantities of different indices to ether equivalent oneSy 

 that shall have a common index* 



RULE. 



I. Divide the indices of the quantities by the given in- 

 dex, and the quotients will be the new indices for those 

 quantities. 



2. Over 



