150 ARITHMETIC. 



proposed, either reduce it to an improper fraction, or re- 

 duce the vulgar fraction to a decimal, and proceed by the 

 rule. 



EXAMPLES. 



1. What Is the second power of 45 ? Ans. 2025. 



2. What is the square of '027 ? Ans. '000729. 



3. What is the third power of 3*5 ? Ans. 42*875. 



4. What is the fifth power of .029 ? 



Ans. '000000020511149. 



5. What is the sixth power of 5*03 ? 



Ans. 16196*005304479729. 



6. What is the second power of ~ f Ans. --t 



EVOLUTION. 



The Root of a^y given number, or power, is such a 

 number as, being multiplied by itself a certain number of 

 times, will produce the power ; and it is denominated the 

 jftrst, second, third, fourthy ^c. root, respectively, as the 

 number of multiplications made of it to produce the givers 

 power is o, i, 2, 3, &c. that is, the name of the root is 

 taken from the number, which exceeds the multiplications 

 by I, like the name of the power in involution. 



Note i. The index of the root, like that of the power 

 in involution, is i more than the number of multiplications, 

 necessary to produce the power or given number. ' 



Note 2. Roots are sometimes denoted by writing y/ 

 before the power, with the index of the root against it : 



3 

 so the third root of 50 is -y/ 50, and the second root of it 



is ^ 50, the index 2 being omitted, which index is always 

 understood, when a root is named or written without one. 

 But if the power be expressed by several numbers with 

 the sign + or -— , &c. between them, then a line is drawn 



from 



