Square roots & positive, negative dilema

[khushbumerchant]

Hi, While referring to MGMAT Algebra book, in chapter 4 problem 4 in problem set, I came across a note saying, which is not so very clear to me.

Q: (1/81)^-1/4
Note: On gmat, when given a square root symbol with a number beneath, you are supposed to take only the positive root.

My Query: My confusion out here is, in note the word "number beneath" refers to which number 81 or 4?

[RonPurewal]

Hi, While referring to MGMAT Algebra book, in chapter 4 problem 4 in problem set, I came across a note saying, which is not so very clear to me.

Q: (1/81)^-1/4
Note: On gmat, when given a square root symbol with a number beneath, you are supposed to take only the positive root.

My Query: My confusion out here is, in note the word "number beneath" refers to which number 81 or 4?

The symbol "√" has to have a unique meaning; otherwise it would be useless as a symbol. So, for instance, the expression "√9" refers only to the positive number 3, even though either 3 or -3 can be squared to give 9.
(As for why it's defined this way, think about any application of square roots.
E.g., how long is the hypotenuse of a 45º-45º-90º triangle whose legs have length 1? The answer is √2, but it's only possible to say "the answer is √2" because √2 exclusively represents a positive value.

The same goes for fourth roots, sixth roots, etc. (you know those symbols -- I don't know how to write them here), as well as fractional exponents where the denominator of the exponent is 2, 4, 6, etc.