3^6 ALGEBRA.' 



2. Extract the cube root of ;v*^-j-6;!tf ^— 40;^ ^ -|-96;tf!-«— 6/|^ 

 fc^-{'6x^ — 40A? 2 +96,v — 64(5? * + 2x — 4 



3x^)6, 



,5 



a:^+6^^+i2;c^+8a;^ 



3A;'*) I2A?* 



iV^-J-6/v^ — 40.v3 +96;v — 64 



I z 



Required the square root of a*rj-2^3!^-|-2^^-|-^*+2^^ 

 ^ . Ans. «3-f~^4~^« 



4. Required the ciibe root of a;^ — 6!<;^-\-i^x^ — 2o:v^-{- 

 JiJa;^ — 6x+i, Ans. a;^ — -2a;+i, 



, 5. Required the biquadrate root of i6a^ — g6a^X-\--2i6 

 \(i^x^ — '2i6ax'^'\-^ix'^, Ans. 2«— 3^", 



SURDS. 



Surds are such quantities as have no exact root, being 

 usually expressed by fractional indices, or by means of the 

 radical sign y/. 



X 



Thus, 1^, or Y^2, which denotes the square root of 2. 



And' 3^, or \/'3^j signifies the cube root of the square 

 of 3 ; where the numerator shews the power, to which 

 the quantity is to be raised, and the denominator its root. 



PROBLEM 



