Radical Rules

[kouranjelika]

I know if we have a square root and a square of the same expression, i.e. Sq root of (y-4)^2 = 4 - y; the left side turns into an absolute value: |y-4|

But what if the expression was a lot more simple, i.e.: sq root of n = 2. Logic obviously tells me that n has to be positive since there are no imaginary numbers on the GMAT. and hence if I wanted to know the value of n, this would indeed be sufficient. But I was hesitant because if I assumed that I square both sides of the expression, it becomes |n| = 4. Wouldn't that mean that n could also be negative. Can someone explain?

Thank you!

[RonPurewal]

I know if we have a square root and a square of the same expression, i.e. Sq root of (y-4)^2 = 4 - y; the left side turns into an absolute value: |y-4|

But what if the expression was a lot more simple, i.e.: sq root of n = 2. Logic obviously tells me that n has to be positive since there are no imaginary numbers on the GMAT. and hence if I wanted to know the value of n, this would indeed be sufficient. But I was hesitant because if I assumed that I square both sides of the expression, it becomes |n| = 4. Wouldn't that mean that n could also be negative. Can someone explain?

Thank you!

No, it's just n = 4. You're dealing with two completely different things here.

The point is this: If you square something, then you "lose" the original sign (i.e., it becomes positive, regardless of which sign it started out as). So, then, when you take the square root, you get a number that's the same size as the number you started with"”but always positive. That's why it's an absolute value.
Note that this only happens when you square something and then square-root it.

When you write √n = 2, you are doing no such thing. Plus, "√anything" is already guaranteed to be non-negative anyway, so there is no issue in the first place.

[RonPurewal]

In any case, the following is a good sign:

Logic obviously tells me that n has to be positive since ...

^^ This.
Is what you want to do.

I.e., you don't want to memorize random, non-intuitive rules for pushing meaningless symbols around a page (= what way too many people think math is all about). You want to develop an intuition about it.

[kouranjelika]

Absolutely. I just feel the more advanced stuff I practice and get faced with, the simple stuff like Sq Root of n = 2, starts to look wild :)).

Thanks.

[RonPurewal]

Absolutely. I just feel the more advanced stuff I practice and get faced with, the simple stuff like Sq Root of n = 2, starts to look wild :)).

Thanks.

I know you're being cheeky, but you're actually addressing one of the most important aspects of this test: It's based on ground-level math. If you think too much about "advanced" math, you'll start to neglect basic principles.

In other words, the point is to keep your feet on the ground, so to speak, enough to prevent things from "starting to look wild".

[kouranjelika]

I know, but it's like a catch-22 with this test. Some stuff is so conceptual and obscure, while others are just way too simple that you start to second guess yourself (at least I do myself :)).

I'm about to post a cray cray one in another thread as per the ones I am referring to.

I completely get what you are saying though, we've discussed this before, it's the nature of the beast.

[kouranjelika]

Ron, what topic are you discussing in the Study Hall next week?

[RonPurewal]

Ron, what topic are you discussing in the Study Hall next week?

That decision is normally not made until a couple of hours before the study hall starts.