Confusion on when to put ± sign

The \pm sign definitely can cause a lot of confusion for students. For starters,

|x|=\pm{x}
x^{2}={|x|}^2

and the list goes on.

So my focus today is to explain when to put \pm while dealing with \sqrt{ }. First, lets recognise a few things.

x=\sqrt{9}: This gives us x=3

x^{2}=9: This gives us x=\pm{3}

Yes, the square-root can be raised to a square for the x, but notice the difference in answer in both cases. The former is a +3 while the latter has -3 too. This is because the square-root is always a positive square-root and does not return \pm{ }. On the other hand, x^{2}={|x|}^2 and the |x|=\pm{x} which causes the \pm{ }.

So next time, please be alert when you introduce the \pm{ }.

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