356 Journal of the Asiatic Society of Bengal, [July, 1908. 
general form. But while his process is perfectly general, it i 
Lei renee in practice nur does it lead to the result in its 
owest term: 
He states ‘that the equation =f (fF, q™ -. etc.) provided 
l, m, m are integers, may be rationalized, ee the rationalized equa- 
tion will be of (k*)th degree, a being the cana of the different 
quantities p, g, 7, etc., andk, the L.C,M, of J, m,n, etc.’ That this 
need not be the case will be evident from the fullowing example :— 
Let amet iit 
then (a—a*) =d 
or a8 —322 +f a+32a—a /a=b 
*, (28+ 32a —b)* = a(32?+ a)? 
whence 2°— is a + 3a°a? ~ 62ab+ b?-—a'=0 which is of the 
sixth de reas Mr. Chattopadhyaya’s method leads to an 
egree. 
ia bees of the Ws Vth, ¢ te, 36th de 
In fact, it will be shown in a subsequent part of = — 
that: if| we rationalize an equation of the form #=a” m4 " +c? 
woe ties be of the mnp.. degree in x 
5. It is easy to see that the most general Gian equation 
t 
involving radicals may be written in the form «=f a . ‘ c”, etc.) 
by taking 2 for the part that is free from radicals. 
To rationalize this, is essentially a problem of elimination, 
= se 
For, if we pat a =y; b"=z; c" =w, and so on, we get 
=I Cae wy eto). 
m= Me 
w* =o 

| 
Equations ( id are sufficient for the elimination of y, z, w, etc., 
because the num of equations is one more than the number of 
variables to be aniaiod So that the problem always admits of 
a a and the result of elimination will be the rationalized 
equa ti 

6. te particular, let us consider the case when 

a= f (a) (1) 
2 
Let a” =y; then y” =a. 
— ne 
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