MULTIPLICATION. 28 1 



So likewise \/ a'^a X V^«+^ =>/a+^ =:«-i"2 *• 



And i^a^x Xx/*^"!"^ =\/j+a? =i:a-|-A; *. 

 And ^a'\'X X\/^+^='2+^- 



These examples shew the grounds, on which the prod- 

 ucts of surds become rational. 



Note 2. Different quantities under the sarnie radical 

 siign are multiplied together like rational quantities, only 

 the product, if it do not become rational, must stand un- 

 der the same radical sign. 



Thus, >/7X\/3=v/7X3=v/2i. 



^"icx y.s/ly z=z^i^cx^ 



And y/4iX\/2^^=>/8^^' =8c'^*!"- 



It may not be improper to observe, that unequal surds 

 have sometimes a rational product. 



As ^^Xv/2 =:y/6^=r8. 



^I2ab y,y/ -^ab Z=:y/'},6a'b''z=.6aL 



V^'y y^^^y'^s/^'y'=<y' 



And v^« 4- ;«)"-'- Xv/fl + xf Xv/^4-;ff 



n'—r\T 



CASE 



M M 



