This is a very good question.  We need to be very clear about the meanings of the definition of square roots and the notation we use for them.

Each positive number $a$ has two square roots, one positive and one negative.  The number $0$ has only one square root, of course, which is $0$.  When we write the notation $\sqrt{a}$, it represents the nonegative one.  So the square roots of positive number $a$ are $\sqrt{a}$ and $-\sqrt{a}$.  This way, there is no confusion for the expression.

Therefore, whenever you see the expression such as $\sqrt{x^2-3x+2}$, it means the nonnegative square root of $x^2-3x+2$.  It is the same with radicals with even index, such as $\sqrt[4]{m+1}$ and $\sqrt[20]{y^3-3}$: it is required that the value underneath the radical is nonnegative, and the result is also nonnegative.  So $\sqrt[4]{16}=2$, and $\sqrt[6]{-64}$ is undefined in real numbers. For radicals with odd index, there is no such restriction: $\sqrt[3]{-8}=-2$.