44 Algebra. 



' n \a"—b'' 



7. Find the value of 

 S. Find the value of 



y ^a+~x 

 p. Find the cube root of |^^3. 

 One process: ^f73=^|^v/3 (Art. 5) = x?'^| V3, (Art. 7) 



= V|fx3(Art. i8) = 2^J^=2N/i=|v/3. 

 Ayiothcr process; |\/3=v/|4^ (Art. 13) 



10. Find the fourth root oi ^^^x- "^^ ^x^ y\ 



11. Take the cube root of 3'^3. 



12. Take the cube root of v/i. 



7?. Find the value of ' I- |£ 



14. Simplify J_9-^:*, 



Z5. Find the value of (f v^'^|)' x ^^ fv^r 



76. Simplify 





22. Rationalizing Factors. Any multiplier which, when 

 applied to an irrational polynomial, will free it from radicals is 

 called a Rationalizing Factor. Thus 5 — "^3 is a rationalizing 

 factor for the binomial surd 5 + '^3, since {z^-^\^ t^)[^ — \/ 7) — 

 25—3=22. Similarly the rationalizing factor for ^3 — "^5 is 



^3 + ^5. since {%/ t^ — s/ ^){\/ ^-\-s/ ^)= r,.. 3 » n. v^-i"= 



For larger polynomials it may be that the ratfonalizing factor 

 "'^^ is itself composed of several factors. Take the quadratic tri- 



^ V "? nomiai surd ^2 — n^3.^ The rationalizing factor is 

 ^ (v/2 — v/3H-v/7)(2 — 2v/6)for 



(n/2— v/34-x/7)(v/2 — v/3 — v/7)(2 — 2^/6) 



= |(v/2-v/3r~(N/77](2-2N/6) 

 = — i2H-2>/6)(2 — 2V^6)=20. 



