# Thread: Square root Question in doubt

1. ## Square root Question in doubt

Hi Dr.Math,

Recently i have argument with my colleague for equations below

√[(-2)^2] = x

a) x = -2
b) x = 2
c) x = 2 or -2

just wondering which answer of that? a,b or c?

btw, if my equation assignment is

√[(-2)^2] = -2

Can they state my equation with Math Error?

thank you

2. ## Re: Square root Question in doubt

It is simply a matter of the definition of the square root function. Functions of real numbers are always defined so that f(x) has one value for a given x. That is the part of the definition of "function itself". And because of that $\displaystyle \sqrt{a}$ is defined as "the positive number, x, such that $\displaystyle x^2= a$.

Yes, if you are claiming that $\displaystyle \sqrt{(-2)^2}= -2$ you are definitely in error. $\displaystyle (-2)^2= 4$ and $\displaystyle \sqrt{4}= 2$, not -2.

3. ## Re: Square root Question in doubt

Originally Posted by maxowlpang
Hi Dr.Math,

Recently i have argument with my colleague for equations below

√[(-2)^2] = x

a) x = -2
b) x = 2
c) x = 2 or -2

just wondering which answer of that? a,b or c?

btw, if my equation assignment is

√[(-2)^2] = -2

Can they state my equation with Math Error?

thank you
$\displaystyle \sqrt{x^2} = |x|$ ,so if x = -2 ,then $\displaystyle \sqrt{(-2)^2} = |-2|=2$

If x=2,then again $\displaystyle \sqrt {2^2} =|2|=2$