SOLUTIONS TO THE EXERCISES.] MATHEM AT ICS. ALGEBRA. 609 



3 . p rovet]iat 



V/6 4-1/3 3v/2 



V__ __ 



___ 



-y/3) _\/48 y/18 _4y/3 3y/2 

 " "5 5 



4. Prove that - 3 _ ^ 2 = 2 fl/9 + V 6 + V*)- 



2 _ 



S/3 V 2 ~(V 3 V 2 ) 



3-2 



5. Prove that 



= (V + V 35 + V 25). 



Multiplying numerator and denominator by ^/ 49 + j^/ 35 + ^/ 25, we have 



C. Prove that c , & = 11 \/2 4 y^ 15 ^. Multiplying numerator and denominator by 



V 5, 





= 6^2 



1. 



N OF THE CUBE BOOT PAGE 486. 



j' + g^ + fcr 4 99* 1 

 of 



9* + 6j< 99*3 



2U 4 126x' 



21z* 126x 



343 



343 



3* 3 



3x 



3^ + 3^ 

 3j 



3* 2 + 6* 

 3x 



21* J 63*+ 49 



18*' + 6.t J 63* + 49 



3* 5 + 9.r 



7 



3x J + 9 7 Hence the cube root of the proposed polynomial ig *' + 3z 7. 



8. 



C4 



64 



2.Z 



3x 3 + 2z 

 2* 



3* 2 + 4x 3* 4 -f 12* 3 + 0a' 24* + 16 

 2* 



3*' + 6* 



4 



4 Hence the cube root is 4p + 2r 4. 



t Thli i of no vtlne, and merely completes the series of er poncnts ol x. 



Sec the .Vote appended to the last example In thi Key. 



