general query

[ruplun]

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

[Anurag@Gurome]

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.

[ruplun]

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

[Ian Stewart]

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' (√), by definition that produces only the non-negative square root of what is underneath. So if you see something like √4, 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 √n denotes the positive number whose square is n').

[edvhou812]

I got x=3y for the answer. Can someone confirm or correct?