GMAT Square Root Rules

Hi I would like to know about the several rules which have been stated in the Official Guide (OG) of the GMAT examination which one needs to know thoroughly?

[Shaleen]

Have you ever gotten a GMAT address wrong since you thought you should take a square root and get two unique numbers yet the answer key said just the positive root checked

On the other hand, have you ever misunderstood one since you took the square root and recorded only the positive root however the answer key said that, this time, both the positive and the negative root tallied

There are a few tenets we have to keep straight as far as how government sanctioned tests (counting the GMAT) manage square roots. The Official Guide details these standards, however enough understudies have addressed about the OG clarification

Doesn't the OG say that we're just expected to take the positive root?

Once in a while this is genuine " yet not generally. This is the place the disarray emerges. Here's a quote from the OG thirteenth version

Each positive number n has two square roots, one positive and one negative, however √n signifies the positive number whose square is n.

the main half appears to be very clear that, in the event that you take the square root, you ought to get two qualities. The second 50% of the sentence is somewhat befuddling however.

For example, √9 denotes 3. [However] The two square roots of 9 are √9 = 3 and -√9 = -3.

Consider it along these lines: when they give us a square root image with a genuine number underneath it " not a variable " then we ought to take just the positive root. In the event that I approach you for the estimation of √9, then the answer is 3, yet not - 3. That leads us to our first run the show.

Principle #1: √9 = 3 just, not - 3

On the off chance that the issue gives you a real number beneath a genuine square root image, then take just the positive root.

Principle #2: x2 = 9 implies x = 3, x = - 3

How are things diverse in this illustration? We no more have a square root sign " here, we're managing an example. On the off chance that we square the number 3, we get 9. On the off chance that we square the number - 3, we additionally get 9. Along these lines, both numbers are conceivable qualities for x, in light of the fact that both make the mathematical statement genuine.

Principle #3: √(x)2 = 3 implies x = 3, x = - 3

Alright, we're back to our square root sign, however we additionally have an example this time! Presently what? Do we take just the positive root, since we have a square root sign? Alternately do we take both positive and negative roots, since we have a type?