158 ARITHMETiC. 



6. What is the square root of ^ ? 



Ans. '645497. 

 » 



7. What is the square root of 6j ? 



Ans. 2*5298, Sea 



8. What is the square root of 10 ? 



Ans. 3*162277, &c. 



To EXTRACT THE CuBE RoOT* 



RULE.* ^ 



1. Having divided the given number into periods of 3 

 figures, find the nearest less cube to the first period by the 

 table of powers or trial 5 set its root in the quotient, and 

 subtract the said cube from- the first period ; to the re- 

 mainder bring down the second period, and call this the 

 resolvend. 



2. To three times the square of the root, Just found, 

 add three times the root itself, setting this one place more 

 to the right than the former, and call this sum the divisor. 

 Then divide the resolvend, wanting the last figure, by Ihe 

 divisor, for the next figure of the root, which annex to the 

 former ; calling this last figure e^ and the part of the root 

 before found call a, 



q, Add 



* The reason of pointing the given number, as directed in the 

 rule, is obvious from Cor. 2, to the Lemma made use of in de- 

 monstrating the square root ; and the rest of the operation will 

 be best understood from the following analytical process : 



Suppose N, the given number, to consist of two periods, and let 

 the figures in the root be denoted by a and b. 



Then 



