# Linked Questions

5answers
698 views

### 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 ...
4answers
22k views

### 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 $x ≥ 2$ ...
2answers
7k views

4answers
647 views

### 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.
2answers
383 views

### 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 $\sqrt{x^2} = \pm x$?
3answers
68 views

### Square roots: $-\sqrt{a} = \sqrt{b}$ [duplicate]

[CLOSED] Thanks GoodDeeds and Henry  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 ...
2answers
60 views

### 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 \$...
0answers
34 views

### Is there an application to NOT assuming that a square root is positive?

Further to the question here:Why is the even root of a number always positive? If it is mere "convention" (agreement) that we use positive real numbers as the even-powered-roots of positive real ...