<s>[INST] Does $2^2=4$ imply $2=\pm \sqrt{4}$? I read the square root property from the book, College Algebra by Raymond A Barnett and Micheal R Ziegler that,
The square root property says,

If $A^2=C$ then $A=\pm \sqrt{C}$

I took the equality,
$2^2=4$ 
$\implies 2=\pm \sqrt{4}$
$\implies 2=\pm {2}$
but, How $2$ can be equal to $-2$?
 [/INST] Let's see how "If $A^2=C$ then $A=\pm \sqrt{C}$" is obtained:
$A^2=C \Rightarrow A^2-C=0 \Rightarrow (A-\sqrt{C})(A+\sqrt{C})=0 \Rightarrow$ 
$A-\sqrt{C}=0$ or $A+\sqrt{C}=0 \Rightarrow A_1=\sqrt{C}$ or $A_2=-\sqrt{C} \Rightarrow A=\pm \sqrt{C}$.
Now let's see what happens to "$2^2=4$":
$2^2=4 \Rightarrow 2^2-4=0 \Rightarrow (2-\sqrt{4})(2+\sqrt{4})=0 \Rightarrow$ 
$2-\sqrt{4}=0$ or $2+\sqrt{4}=0 \Rightarrow 2=\sqrt{4}$ or $2\ne-\sqrt{4} \Rightarrow 2=\sqrt{4}$.
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