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PP2:sqr rt X^2/X: [X]/X or X/X? Bc OG pge 37 says sqr rt X

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storme
 Post subject: PP2:sqr rt X^2/X: [X]/X or X/X? Bc OG pge 37 says sqr rt X
 Post Posted: Wed May 14, 2008 4:01 am 
Question is: what is sqre root X^2/X.
ans: absolute X/X and not X/X=1.

i understand that sqre's have 2 root values BUT OG 10th Edition page 37 says that square root of the positive integer N denotes the POSITIVE number whose sqre in N.
So lets says N=3, that would be sqre root 9/3
= the POSITIVE sqre root of 9/3 =1.

so my confusion is WHEN is the root denoted as POSITIVE...bc i see why sqre root 9 could have 2 roots but that OG comment has confused me about when the exception might be the case - i.e when is it only definitely the positive sqre root?
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RonPurewal
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 Post Posted: Wed May 14, 2008 6:20 am 
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ManhattanGMAT Staff


Posts: 7146
if you ever see the √ symbol, it always represents the non-negative root.
always.
no exceptions.
(nb: i must say 'non-negative', not 'positive', because √0 = 0 is not positive.)

reason: √ is an operator - it represents a function into which the number is being inputted*. functions always have one value only.

if you have an equation, on the other hand, you can have multiple solutions. for instance, the equation x^2 = 81 has two solutions (9 and -9), even though the operator √81 refers only to positive 9.

--

*yes, 'inputted' is correct. ('input' is also correct as a past participle, but i just don't like the way it sounds or looks)
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