40 Algebra. 



6. 



_576rx-Kr/_ 



7. 2^U—b—V6/^b''-\-6\a'—\2'^ab. 

 14^ To INTRODUCE A COEFFICIENT UNDER THE RADICAI^ 



Sign. It is sometimes convenient to have a radical in a form 

 without a coefficient. The coefficient can always be introduced 

 under the radical sign by the inverse of the method of Art. 8. 

 Thus, 2%"^ 2ax=-^ % x'^'^ 2ax=^'^^ ibax^ \ similarly, a\^ c='s/a"c. 



15. ExAMPi.ES. Place the coefficients in the following under 

 the radical sign without changing the value of the expression : 



7. T^ax^^y 2>^^' 



K6- 

 x^a—x. 



50^50- 



a~b^>/ X — 



y- 



16. Addition and Subtraction of Radicai^s. Similar rad- 

 icals (Art. 4) can be combined by addition or subtraction ; and if 

 they are dissimilar no combination can take place. Take for ex- 

 ample the expression, 



Reducing each expression to its simplest form, it becomes 

 ax^'yT^a-\-\\^io—^ax^\^2>^-\-\^ 10. 

 It is now noticed that the first and third and the second and 

 fourth radicals are similar to each other ; whence, grouping sim- 

 ilar terms, the expression becomes 



(ax'-lax')s^2>^ + (i^l)\^io, 

 or \ax''>/ 2>^-\-i\\^ 10. 

 We observe here the necessity of reducing each of the radicals in 

 any given expression to its simplest form, for then it can be 

 told whether or not any number of the radicals are similar to 

 each other and consequently whether or not they can be combined 

 together. 



