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ruplun: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jun 18, 2010 7:09 am; Thanked: 1 times; Followed by:2 members

general query

by ruplun » Fri Apr 29, 2011 10:03 pm

In GMAT , is sqaure root of a integer is considered positive always? and if x^2 = 9y^2 , what is the value of x , please do let me know

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Source: Beat The GMAT — Problem Solving | Fri Apr 29, 2011 10:03 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Fri Apr 29, 2011 10:47 pm

ruplun wrote:In GMAT , is sqaure root of a integer is considered positive always? and if x^2 = 9y^2 , what is the value of x , please do let me know

You are right, the sqaure root of an integer is considered positive.

Last edited by Anurag@Gurome on Sat Apr 30, 2011 1:12 am, edited 1 time in total.

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ruplun: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jun 18, 2010 7:09 am; Thanked: 1 times; Followed by:2 members

by ruplun » Fri Apr 29, 2011 11:12 pm

but we can write x^2 - 9y^2 = (x+3y)(x-3y)=0, in that case values is, 3y,-3y...which is correct?

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by Ian Stewart » Sat Apr 30, 2011 10:48 am

The above post is not correct; a positive number has two square roots. The square roots of 4 are 2 and -2, because 2^2 and (-2)^2 are both equal to 4. However, when you see the 'square root symbol' (âˆš), by definition that produces only the non-negative square root of what is underneath. So if you see something like âˆš4, that is equal to 2 (and never to -2).

You might look at pg. 114 of OG12 ('every positive number n has two square roots, one positive and the other negative, but âˆšn denotes the positive number whose square is n').

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