What is the principal square root of x?

Answer 1

It is the positive square root of x.

Answer 2

Restricting the discussion to real numbers for now. In this case, the square root is only defined for non-negative numbers; the principal square root of a positive number is the POSITIVE square root. For example, both +5 and -5 are square roots of 25, since both - when squared - give you 25. But the positive square root (+5) is called the principal square root, and if you write the square root symbol, that's the number usually meant.