Problem Solving

Actually Amitava is right, the sqrt of a number until unless mentioned should be considered positive. While you are right that any integer has 2 roots, we consider only the positive root (the principal root) for solving problems such as these. So Amitava's answer is right i.e m>4. There is no ambiguity in the answer choices.

Do a google search on "principal square root" and you will find articles on why this is so.

Regards

FIrst, all you guys are great at catching such subtle details. I am a bit confused now, I see Mr. Daemon's point but see moderators point also. For the sake of the exam, are we considering all roots positive? I believe this is what is taught in the manhattan gmat book also.

AS for the original question, I think the original poster is hurting from understanding that all fractional exponents are treated as roots. I had to make a flash card on this to commit it to memory. Recommendations to you also.

Enginpasa1 wrote:FIrst, all you guys are great at catching such subtle details. I am a bit confused now, I see Mr. Daemon's point but see moderators point also. For the sake of the exam, are we considering all roots positive? I believe this is what is taught in the manhattan gmat book also.

AS for the original question, I think the original poster is hurting from understanding that all fractional exponents are treated as roots. I had to make a flash card on this to commit it to memory. Recommendations to you also.

It is not just for GMAT, but for math in general we consider only the principal roots that is the positive roots of any real number. There are many reasons for this e.g. use of square roots in the Pythagoras theorem.

Regards

Gabriel,
For discreet values given as choices, of simple functions, we can use the principle sq root. But, when the range of values is required then you may have to use both the values. And that is what is the case in the given problem.

i guess we have to get it by heart - to use +ve root for GMAT unless required specifically.

Yes by convention, sqrt(x) is always positive. Because of this, the answer must be greater than 4.