If you're experiencing a roadblock with one of the Manhattan Prep GRE math strategy guides, help is here!
rohan.karandikar
Students
 
Posts: 1
Joined: Mon Oct 14, 2013 12:42 pm
 

5 lb. book, Chapter 14, Question 4 (error?)

by rohan.karandikar Wed Nov 13, 2013 9:01 pm

Chapter 14, Question 4 on page 551 is about exponents and roots:

Quantity A
square-root(3) + square-root (6)

Quantity B
square-root (9)

THEIR answer: Quantity A because...
"You may NOT add root(3) and root(6) to get root (9), but you can simply put each value in your calculator. Root(3)=1.732... and root(6)=2.449..., and their sum is 4.18. Since Quantity B is root(9)=3, quantity A is larger."

I see a problem with this logic because root(3) = +/- 1.732 and root(6) = +/- 2.449, whereas root(9) = +/- 3, which means that when added you have four options for Quantity A (+/- 4.181 and +/- 0.717) and two for Quantity B (+/- 3), hence it is impossible to tell, hence my answer would be D.
Now there are NO absolute signs anywhere on this problem.
Are we, on the real GRE, NOT to consider that for a root there are two solutions?

Thanks in advance for your help.
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: 5 lb. book, Chapter 14, Question 4 (error?)

by tommywallach Fri Nov 15, 2013 6:32 pm

Hey Rohan,

Actually, this is a very standard misunderstanding. The square root of a positive number is by definition only the positive root (one solution). The square root of 9 is, by definition, only 3. The only time you get two solutions is when you square root an expression containing a variable.

-t