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### Why is $\sqrt{4} = 2$ and Not $\pm 2$? [duplicate]

I've always been told that if $\ x^2 = 4,$ $=>x = \pm2$ But recently, Prof. mentioned that if $x = \sqrt{4}$, Then $x = +2(only)$ I am very skeptical about this because they both mean the ...
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### Is sqrt(x) a function? Does it matter if a domain is given? [duplicate]

Possible Duplicates: Reason why the even root of a number always positive Square roots — positive and negative I saw the following during a practice exam: $f(x) = \sqrt x$ for $x ≥ 2$ ...
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### Why does Wolfram Alpha say that $\sqrt{1}=-1$? [duplicate]

Why does Wolfram Alpha say that $\sqrt{1}=-1$? Is this a mistake or what? Can anyone help? Thanks in advance.
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### Why does the square root of a square involve the plus-minus sign?

If $\sqrt{x^2}$ can be simplified as follows: $\sqrt{x^2} = (x^2)^\frac{1}{2} = x^{\frac{2}{1}\times\frac{1}{2}} =x^\frac{2}{2} = x^1 = x$ Then why would $\sqrt{x^2} = \pm x$?
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### Square roots: $-\sqrt{a} = \sqrt{b}$ [duplicate]

[CLOSED] Thanks GoodDeeds and Henry [1] I understood the fundamental problem. As √9 = ± 3 If , √A = √B Thus, ** ±a = ±b** And so a = b; -a = b; and a = -b;; Thus, √9 = +3 OR -3 Let, √A = ±a ...
### Find $f(g(x))=-\sqrt{x}$ where $f(x) =\sqrt {x}$
If we have $f(x)=\sqrt{x}$ Find $g(x)$ where $f(g(x))=-f(x) =-\sqrt{x}$ I know that the square root can have plus and minus value in the same time but I what that $f(g(x))$ value is negative when \$...