SOLUTION: Simplify each expression. Rationalize all denominators. Assume that all variables are positive. http://i732.photobucket.com/albums/ww330/school_hard/IMG_48371.jpg http://i7

Algebra ->  Rational-functions -> SOLUTION: Simplify each expression. Rationalize all denominators. Assume that all variables are positive. http://i732.photobucket.com/albums/ww330/school_hard/IMG_48371.jpg http://i7      Log On


   

Question 182355: Simplify each expression. Rationalize all denominators. Assume that all variables are positive.

http://i732.photobucket.com/albums/ww330/school_hard/IMG_48371.jpg
http://i732.photobucket.com/albums/ww330/school_hard/IMG_48381.jpg
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
5sqrt%2832%29+-+7sqrt%288%29
Begin by factoring terms inside the radical (w/prime numbers):
5sqrt%282%2A2%2A2%2A2%2A2%29+-+7sqrt%282%2A2%2A2%29
Then, pull out "pairs" from under the radical:
5%282%2A2%29sqrt%282%29+-+7%282%29sqrt%282%29
20sqrt%282%29+-+14sqrt%282%29
Factoring:
sqrt%282%29%2820+-+14%29
sqrt%282%29%286%29
6sqrt%282%29
.
.
.
2sqrt%2815xy%5E3%29+%2A+sqrt%2830x%5E3y%5E2%29
Pull out pairs:
%282y%29sqrt%2815xy%29+%2A+xy%28sqrt%2830x%29%29
%282xy%5E2%29sqrt%2815xy%29+%2A+sqrt%2830x%29
%282xy%5E2%29sqrt%2815xy30x%29
%282xy%5E2%29sqrt%2815xy%282%2A15%29x%29
2xy%5E2%2815x%29sqrt%282y%29
%2830x%5E2y%5E2%29sqrt%282y%29