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GRE Algebra http://www.800score.com/forum/viewtopic.php?f=12&t=14130 
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Author:  questioner [ Thu Nov 15, 2012 5:43 pm ] 
Post subject:  GRE Algebra 
Please explain how this equation works out: s² / (s²√3 / 4) = 4s² / (s²√3) = 4 / √3 = (4√3) / 3 I am with each step, crossing out the s², and then you have 4 / √3. But how does 4 / √3 turn into 4√3 / 3? Isn't that an extra three? I think what I really need is a lesson in multiplying/dividing by radicals. I always seem to mess them up and the only thing I ever read is telling me to group radicals together and treat regular numbers separately. I do not see anything that goes into depth. Please help! 
Author:  Gennadiy [ Thu Nov 15, 2012 6:03 pm ] 
Post subject:  Re: GRE Algebra 
Quote: But how does 4 / √3 turn into 4√3 / 3? Isn't that an extra three? This is the method to eliminate radicals in a denominator.We multiply the numerator and denominator by the same number, √3. 4 / √3 = 4√3 / (√3 × √3) The denominator, √3 × √3, results in (√3)² = 3 . So we get: 4 / √3 = (4√3) / 3 Quote: I always seem to mess them up and the only thing I ever read is telling me to group radicals together and treat regular numbers separately. If you are Ok with exponents, then you can treat radicals as exponents.√a is a to the (1/2)th power Another two simple ideas that should get you started on roots are: 1. √a × √a = a ³√a × ³√a × ³√a = a 2. Roots are Ok to multiply in & out (as long as all the numbers under the sign are nonnegative): √(2/3) = √2 / √3 √6 = √(2 × 3) = √2 × √3 √6 / √2 = √(6/2) = √3 or √6 / √2 = √3 × √2 / √2 = √3 If you get the feeling of these two basic concepts, that should allow you to move on to dealing with addition. For example we can transform: √6 + √2 = √2 (√3 + 1). 
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