38 AI.GEBRA. 



6. s/~^^\ 



' \- xy 



^- X 



- Vax^-\-2X' 



10. s/iSa^b\ 



11. V i92«^jrj^". 



12. VJa — 'by^(b-{-ay^\ 



10. ^o Intkgralize the Expression under the Radicae 

 Sign. Suppose we wish to transform the radical 



3 \ab^ 



so that there shall be no fraction under the radical sign. Multi- 

 ply both numerator and denominator of the fraction by a quantity 

 that will render the denominator a perfect cube, thus : 



3 \ab^ 8 lab' x^y_^ \ab^x^^ 



\xy-~'Sixy'' x^y \ x'^y'^ 



— = ^ = , "^ 



\xy- ^ixy"" x^y \ x'^y 



But, by Art, 6, 



3 I ah'x ^y _ ^' ab\x^~y _ i 



In general, to integralize a radical of the form |--, multipl; 



numerator and denominator by b" ' and we obtain 



« lab"^' 



^l b" ' 



which, by Art. 6, equals 



'Vb" ' 



and this is equal to 



~s/ab , 



which is in the required form. 



