What is Square root of x squared

Question

My apologies if it is redundant question (& a silly one). But here it is, if someone could care to explain:

If Square root of x squared = Mod of x ... doesn't it mean the result is always a positive valued x (because of the modulus)?

OR

is it: Square root of x squared = Plus or Minus (Mod of x)?

p.s: I am sorry, but I don't know how to use the forum buttons for modulus and square root/square of a number. I'd appreciate if someone could also enlighten me with those buttons

Bunuel · Answer

About \sqrt{x^2}=|x| . The point here is that as square 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? The absolute value function: |x|=x , if x\geq{0} and |x|=-x , if x<0 . That is why \sqrt{x^2}=|x| . Hope it's clear. P.S. Writing Mathematical Formulas on the Forum: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

Blackbox · Answer

Thank you, my dear sir!

What is Square root of x squared

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