Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Actually the question is pretty straight forward, however upon further examination I somehow got confused on the "well-known" fact that anything you do to one side of an algebraic equation, you must do to the other side. I'll try to elaborate with an example:

Given that √(3b-8) = √(12-b), what is b?

I understand that the approach is to cancel both radicals, and then just proceed with a very simple equation. However in strict theory, wouldn't you have to multiply what you do to one side, to the other side as well?

√(3b-8)^2 = √(12-b) * √(3b-8)

I know I am completely wrong, but it is probably only a matter of having too much of this GMAT stuff. Thanks to anyone that will kindly respond to my inquiry.

Re: Elimination of radials - Confused¿? [#permalink]

Show Tags

05 Sep 2012, 15:14

1

This post received KUDOS

Patheinemann wrote:

Actually the question is pretty straight forward, however upon further examination I somehow got confused on the "well-known" fact that anything you do to one side of an algebraic equation, you must do to the other side. I'll try to elaborate with an example:

Given that √(3b-8) = √(12-b), what is b?

I understand that the approach is to cancel both radicals, and then just proceed with a very simple equation. However in strict theory, wouldn't you have to multiply what you do to one side, to the other side as well?

√(3b-8)^2 = √(12-b) * √(3b-8)

I know I am completely wrong, but it is probably only a matter of having too much of this GMAT stuff. Thanks to anyone that will kindly respond to my inquiry.

An equality, you can also raise to some power. If for two non-zero numbers \(A=B\), then multiplying both sides by \(A\) we obtain \(A\cdot{A}=AB\) but \(A=B\), so \(A^2=B^2.\) You can continue and obtain that for any positive integer \(n, \, A^n=B^n.\)

What you have written is true, but it won't help you get rid of the radicals the way it is written.

If two numbers are equal, raised to the same power will remain equal. You do the same to both sides of the equation, you raise them to the second power.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Actually the question is pretty straight forward, however upon further examination I somehow got confused on the "well-known" fact that anything you do to one side of an algebraic equation, you must do to the other side. I'll try to elaborate with an example:

Given that √(3b-8) = √(12-b), what is b?

I understand that the approach is to cancel both radicals, and then just proceed with a very simple equation. However in strict theory, wouldn't you have to multiply what you do to one side, to the other side as well?

√(3b-8)^2 = √(12-b) * √(3b-8)

I know I am completely wrong, but it is probably only a matter of having too much of this GMAT stuff. Thanks to anyone that will kindly respond to my inquiry.

Take some numbers to understand this. The equality sign means that whatever is on the left hand side, it is equal to whatever there is on the right hand side. So if the LHS is 2, RHS is also 2

2 = 2 Now, you can square both sides and the equality will still hold 2^2 = 2^2 You can raise both sides to any power, the equality will hold.

You can also multiply the same number on both the sides, the inequality will still hold 2*3 = 2*3

You can choose to do whichever operation suits your purpose. Since you want to get rid of the root sign, you would want to square both sides.

Also, notice that here √(3b-8)^2 = √(12-b) * √(3b-8), √(3b-8) = √(12-b) (even though they don't look same but they are since it is given to us) so √(3b-8)^2 = √(12-b) * √(3b-8) is the same as √(3b-8)^2 = √(12-b)*√(12-b)
_________________

Re: Elimination of radials - Confused¿? [#permalink]

Show Tags

09 Sep 2012, 08:45

Patheinemann wrote:

Actually the question is pretty straight forward, however upon further examination I somehow got confused on the "well-known" fact that anything you do to one side of an algebraic equation, you must do to the other side. I'll try to elaborate with an example:

Given that √(3b-8) = √(12-b), what is b?

I understand that the approach is to cancel both radicals, and then just proceed with a very simple equation. However in strict theory, wouldn't you have to multiply what you do to one side, to the other side as well?

√(3b-8)^2 = √(12-b) * √(3b-8)

I know I am completely wrong, but it is probably only a matter of having too much of this GMAT stuff. Thanks to anyone that will kindly respond to my inquiry.

For such question to solve, firstly try to form simple equation. For this we need to get out of that square root. Now, if a=b, then \(a^2 = b^2\)(squaring both sides) In our case, \(\sqrt{(3b-8)}^2 = \sqrt{(12-b)}^2\) -->> \(3b-8=12-b\) -->> \(4b=24\) -->> \(b=24/4=6\) Therefore, b=6
_________________

My mantra for cracking GMAT: Everyone has inborn talent, however those who complement it with hard work we call them 'talented'.

+1 Kudos = Thank You Dear Are you saying thank you?

Re: Elimination of radials - Confused¿? [#permalink]

Show Tags

20 Mar 2017, 03:24

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...