Data Sufficiency (DS) | Re: Is (x + y)^2 > x^2 + y^2?

MUST KNOW: \(\sqrt{x^2}=|x|\):

The point here is that sincesquare root function cannot give negative result then\(\sqrt{some \ expression}\geq{0}\) .

So\(\sqrt{x^2}\geq{0}\) . But what does\(\sqrt{x^2}\) equal to?

Let's consider following examples:
If\(x=5\) -->\(\sqrt{x^2}=\sqrt{25}=5=x=positive\) ;
If\(x=-5\) -->\(\sqrt{x^2}=\sqrt{25}=5=-x=positive\) .

So we got that:
\(\sqrt{x^2}=x\) if\(x\geq{0}\) ;
\(\sqrt{x^2}=-x\) if\(x<0\) .

What function does exactly the same thing?
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