Problem solving approach in Chapter on "Roots"

[apratim2002]

In one particular book, the Number Properties Guide, I found that the concept used to solve problems on "Roots" doesn't seem correct. Only the positive square roots are being considered in solving the problems, whereas taking the square root of a number will always produce both a positive solution and a negative solution. That can make a lot of difference. Let's consider a specific case : "Number Properties" Strategy Guide (Guide 4, 3rd Edition), Page 109, Problem number 2.It says 36<x<49. And then we have a comparison question. The solution on page 111 says that square root of x should be between 6 and 7. But that doesn't seem complete. Square root of x can also be between -7 and -6. And in that case, Quantity B would be greater. So The correct answer should have been D (Cannot be determined). This is the way all the problems in the chapter on "Roots" have been solved. I even tried a few problems on the same chapter from "5LB Book of GRE Practice Problems". Even there a similar approach has been taken. Not only does it seem wrong, it is also inconsistent with strategies followed in the rest of the chapters. In other chapters, whenever a square root had to be taken, both the positive and negative roots have been considered. It has even been shown in some chapter that if we do not consider the negative solution as well, it could well be the difference between a wrong answer and the right one.
Please let me know if I'm missing something here. Is the inconsistency justified? If so, how? And how do we know during the exam which approach to follow?

[tommywallach]

Hey Apratim,

Indeed, this is one of the mysterious issues of math. The square root of a positive number does not create two solutions. The definition of a square root is that it is only positive. So square root of 49 is only 7, not 7 and -7.

The issue of two solutions DOES come up, but it only comes up when you square root an expression featuring a variable.

x ^ 2 = 49

NOW, x can equal 7 or -7.

But if you are only square rooting a number, the square root is always positive.

Strange, I know, but true. More here: http://www.manhattangmat.com/forums/neg ... 14759.html

-t