fiVOLUTIOK, 



:*55 



6. Find a divisor as before, by doubliag the figures al- 

 ready in the root 5 and from these find the nejct figure of 

 the root, as in the last article ; and so on through all the 

 periods to the last. 



Note i. When the root is to be extracted to a great 

 number of places, the work may be much abbreviated thus : 

 having proceeded in the extraction by the common method 

 till you have found one more than half the required num- 

 ber of figures in the root, the rest may be found by divid- 

 ing the last remainder by its corresponding divisor, annex- 

 ing a cypher to every dividual, as in division of decimals ; 

 or rather, without annexing cyphers, by omitting continu- 

 ally the right hand figure of the divisor, after the manner 

 of contraction in diyision of ^decimals. 



Note 2. By means of the square root we readily find 

 the fourth root, or the eighth root, or the sixteenth root, 

 &c. that is, the root of any power, whose index is some 

 power of the number 2 ; namely, by extracting so often 

 the square root, as is denoted by that power of 2 ; that is, 

 twice for the fourth root, thrice for the eighth root, and 

 so on. 



To EXTRACT THE SQUARE Ro.OT OF A VUL- 

 GAR Fraction. 



RULE. 



First prepare all vulgar fractions by ^reducing them to 

 their least terms, both for this and all other roots. Then 



1. Take the root of the numerator and that of the 

 denominator for the respective terms of the root required. 

 And this is the best way, if the denominator be a complete 

 power. But if not, then 



2. Multiply the numerator and denominator together 5 

 take the root of the product : this root, being made the 

 numerator to the denominator of the given fraction, or the 



f denominator 



