RaDICAIvS. 



43 



ly. Multiply 3 — v^6 by >/ 2—^/3. 



Process. 



3- ^6 

 \/ 2— v/3 



3^^2 — 2V/3 



6^/: 



-3^3 + 3^2 

 ^-5^3 



Result. 



Find the value of 

 18. (v/3-v/;)(n/3 + n/2). 

 /p. (2V/5 — 3\/2 + v^ io)('v^i5 — v/6). 



pz. (3n/45 — 7x/5).(v/7|+2v/9|). 



20. Powers and RooTvS of Radicals. It has already been 

 shown (Chapter II) that we can raise a quantity affected by a 

 fractional exponent to any required power by multiplying the 

 fractional exponent by the exponent of the required power. It 

 was also shown that any root of a quantity affected with a frac- 

 tional exponent could be found by dividing the fractional ex- 

 ponent by the index of the required root. Hence we can find 

 any power or any root of a radical if it is expressed by means of 

 fractional exponents ; but of course in the simpler ca.ses the con- 

 venience of fractional exponents will not be felt. We give one or 

 two illustrations and leave the student to his own method ; the 

 chief requirement is that he should be able to show that his work 

 is established on sound principles. 



The result should appear in its simplest form. 



21. Examples. 



1. Square |^a^. 



Process: {^^a^Y=^[^^d'y^^,^a'=^^a^^a. 



2. Find the fourth power of ^v^'^12. 



3. Cube 



S a' 



4- 

 5- 

 6. 



Square 3*^3. 

 Square \^ 2. 

 Cube axs^ ax. 



