Negative Square Root

Hi melguy.

From what I can see you provided the answer to your own question without realizing it.

Your information indicates that the x in x² = 11 could be negative or positive, while √11 is always positive.

Doesn't that answer your question?

You're right that the GMAT won't allow "negative square roots", but let's be sure to clarify what those are.

-√11 is a negative square root, but the GMAT is fine with this number.

√(-11) is a "negative square root", but the GMAT is NOT fine with this number.

The crucial difference comes when the negative sign is INSIDE the square root. Any √(negative) is not recognized by the GMAT, and can be ignored, but -√(positive) is fine.

So in your question, x² = 11 DOES have two solutions that the GMAT will recognize: x = √11 and x = -√11. But x² = -11 has NO solutions that the GMAT will recognize, since its roots are x = √-11 and x = -√-11.

It's also worth mentioning that the GMAT only recognizes positive square roots when the square root term appears. So

x² = 121

has two roots, x = 11 and x = -11.

But x = √121 only has ONE root, x = 11. This seems so random, but the GMAT will be consistent about it, so any time a √ appears, you only need to consider the nonnegative roots. (In other words, if a DS question says "x = √121", you can say that x has one and only one solution, x = 11.)

Hi Marty

I actually thought -√11 and √(-11) meant the same thing. Hence the confusion.

CC Matt: Thanks a lot for clearing out the confusion!