SURDS. 325 



V 5. Required the 4th power of ^V6. Aug. yg-. 



^. It is required to find the wtji power of a'\ 



PROBLEM IX. 



To extract the roots of surd quantities^ 



RULE.* , 



Divide the index of the ^iven quantity by the index of 

 the root to be extracted ; then annex the result t;o the roo^ 

 of the rational part, and it will give the root required. 



EXAMPLES. 



3' 

 I, It is required to find the square root of 9^/3. 



First, Vpzis ; 

 And3^l^z::r3^-^'=3^; 



Therefore ^^2 I ^^3 X3^ is the square root required. 



2. It 



* The square root of a binomial or residual surd, A-^-B, ox 

 4— 'By may be found thus : take V-^^ — B^z=:D ; 



Then ^jT^-^t±^J^j±i:^^ 



2 2 



A-^^D ,A^D 



And V A^B=J-^ J 



"2 "2 



Thus, the square root of 8+2-v/7=i + v^7 ; 



And the square root of 3 — ^/%z=:.yj 2 — i ; 



Jut for the cube, or any higher root, no general rule is giveni 



