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Would we not consider (-2)^2 = (2) ^2?Thus ideally (x^1/2)^2 has 2 roots:+x and -x. But from the OG problems that I have seen,we consider only the positive root.An example will be D.S. Q 260 on OG 10th edition.

MA, I disagree when u say square root of 4 is only +2. Every positive number has two square roots, one positive and one negative. Both 2 and
-2 are square roots of 4.

This can be a typical DS question: x is an integer, is x = 3 ?

1) x^2 = 9 .....Here we get 2 values +3 and -3 thus insufficient.

However, understanding Anna ques now, it is true that when we use a radical sign i.e. square root sign, by definition, it means the principal or positive sqaure root only, thus as Anna said:

Thank you for your response.For folks who are interested in why we assume positive root for radical sign i.e. square root sign,please refer to the following link:
http://www.jamesbrennan.org/algebra/rad ... _roots.htm ++++

Quote:
To avoid confusion between the two we define the symbol (this symbol is called a radical) to mean the principal or positive square root.

The convention is:

For any positive number x,

(x)^1/2 is the positive root, and

-(x)^1/2 is the negative root.
+++

Rgds,
Anna

banerjeea_98 wrote:

MA, I disagree when u say square root of 4 is only +2. Every positive number has two square roots, one positive and one negative. Both 2 and -2 are square roots of 4.

This can be a typical DS question: x is an integer, is x = 3 ?

1) x^2 = 9 .....Here we get 2 values +3 and -3 thus insufficient.

However, understanding Anna ques now, it is true that when we use a radical sign i.e. square root sign, by definition, it means the principal or positive sqaure root only, thus as Anna said:

MA, I disagree when u say square root of 4 is only +2. Every positive number has two square roots, one positive and one negative. Both 2 and -2 are square roots of 4.

This can be a typical DS question: x is an integer, is x = 3 ?

1) x^2 = 9 .....Here we get 2 values +3 and -3 thus insufficient.

However, understanding Anna ques now, it is true that when we use a radical sign i.e. square root sign, by definition, it means the principal or positive sqaure root only, thus as Anna said: