326 ALGEBRA. 



2. It is required to find the cube root of ■g-V^2, 

 First, \<^=i ; 



And "i/7F= z^'^^zz 2^ ; 



Therefore ~^2\'^ z=:^X^^ is the cube root required. 



3. Required the square root of lo^ Ans. icv/io.. / 



4. Required the cube root of ~a^. Ans. fa.l 



5. Required the 4th root bf 3a;''» Ans. s'^X.a?^. 



INFINITE SERIES. 



. An infinite series is formed from a fraction, having a 

 compound denominator, or by extracting the root of a 

 surd quantity ; and is such aSj being continued, would rua 

 -on infinitely, in the manner of some decimal' fractions. 



But by obtaining a few of the first terms, the law of 

 the progression will be manifest, so that the series may be 

 continued without the continuance of the operation, by 

 which the first terms are found. 



- PROBLEM I. 

 21? reduce fractional quajitities to infinite series* 

 RULE. 



Divide the numerator by the denominator ; and the op- 

 eration, continued as far as may be thought necessary, will 

 give tliC series required. 



EXAMPLES, 



