Square root of a square I'm little puzzled with square roots basics which says that square root of a squared number is absolute value of that number. I was in a impression that it would have both positive and negative roots.For example
The Basic says: $\sqrt{2^2} = |2| = 2$
While I think that: $\sqrt{2^2} = \sqrt{4} = 2$ or $-2$.

$\sqrt{a^2}=|a|=a$. This is because the square root function returns the principal (positive) root.
Note that both $a\times a$ and $-a\times-a$ equal $a^2$ though.
You may be wondering when do we use the above fact. An example is when solving a quadratic equation:
Solve for $a:$ 
$(a^2-2)=0\implies a^2=2\implies a=\sqrt{2}$ or $a= -\sqrt{2}$
So to summarize, when dealing with the square root, the principal root is returned, while solving for variables, you can consider all values for which the equation holds.
