Most of the questions from the official GMAT download are posted, but I could find this one. Any help explaining how to do this would be great. My incorrect answer is selected; the correct answer has the box around it. Is it just factored as a quadratic equation? Do the inequalities give you any info needed for solving the problem?

use formula of a^2 - b^2 its (a+b)(a-b)

plug in!! a=6 b=3 on sqrt a^2-b^2 sqrt 36-9 sqrt 27 3 sqrt 3 on statement D (sqrt 9) * (sqrt 3) 3 sqrt 3 same answer!

I am facing same problem.. Even I choose option C... I am not getting whats wrong with C.. Any help would be appreciable.

@ghodke sahab sqrt[(a-b)^2-2ab] =sqrt[a^2+b^2-4ab] which is nowhere equal to a^2-b^2

Hi I think its simple; this uses the below mention formula (a^2-b^2) =(a-b)*(a+b) thanks and regards

Just want to emphasize that you should memorize the basic factoring rules such as (helpful in this example): a²-b² = (a+b)(a-b) Remembering (and being able to apply) these rules is not only handy (as it helps to reduce time spend and errors); I would even say they are essential for some questions. And, after all, there aren't that many to remember: a²-b² = (a+b)(a-b) (a+b)² = a²+2ab+b² (a-b)² = a²-2ab+b² a²+(p+q)a+pq = (a+p)(a+q)

a>b>0 Let a=2 and b=1 So, sqrt a^2-b^2 = sqrt 4-1 = sqrt 3 Now run through the answer choices A. a+b - sqrt 2ab --> 3 - sqrt 2x2 = 3 - 2 = 1 -- Does Not Match sqrt 3 B. a - b + sqrt 2ab --> 1-2 = -1 -- Does Not Match sqrt 3 C. sqrt (a - b)^2 - 2ab --> sqrt -3 -- Does Not Match sqrt 3 D. (sqrt a + b) (sqrt a - b) --> sqrt 3 x sqrt 1 now , sqrt 1 = 1 , so matches sqrt 3 as solved initially.

There's a nice rule that says √(xy) = (√x)(√y) For example √(16*49) = (√16)(√49) = (4)(7) = 28 Since a² - b² = (a + b)(a - b), can use the above rule to conclude that... its √[a² - b²] = √[(a+b)(a-b)] = [√(a+b)][√(a-b)] = D Cheers, Brent

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