SOLUTION: I was working on my homework and this one stumped me. I know there can not be a radical in the denominator and I tried simplifying all of the roots before simplifying it further, b

Algebra ->  Radicals -> SOLUTION: I was working on my homework and this one stumped me. I know there can not be a radical in the denominator and I tried simplifying all of the roots before simplifying it further, b      Log On


   

Question 748277: I was working on my homework and this one stumped me. I know there can not be a radical in the denominator and I tried simplifying all of the roots before simplifying it further, but it is still giving me a bit of trouble and I would love to get help on it.
Could someone please show me how to simplify +sqrt%28+8+%29+ - +sqrt%28+27+%29+/+sqrt%28+6+%29+ - +sqrt%28+5+%29+ ? Thank you for your help!
Answer by timvanswearingen(106) About Me  (Show Source):
You can put this solution on YOUR website!
When solving a problem like this, you need to multiply the top and bottom of the fraction by the conjugate of the denominator.
The conjugate is obtained by simply changing the sign between the two terms of the denominator.
%28sqrt%288%29-sqrt%2827%29%29%2F%28sqrt%286%29-sqrt%285%29%29


Now the bottom will be rationalized:
%28sqrt%2848%29%2Bsqrt%2840%29-sqrt%28162%29-sqrt%28135%29%29%2F%286-5%29

%28sqrt%2848%29%2Bsqrt%2840%29-sqrt%28162%29-sqrt%28135%29%29%2F1
You can simplify the radicals a bit on top if you'd like, but it won't look much prettier. That's it for rationalizing the denominator.