TITLE: Can the square root of a real number be negative?
QUESTION [22 upvotes]: Can the square root of a real number be negative?
Dealing with the questions of functions in eleventh class my maths teacher says that square root of a real number is always positive. How is it possible?

REPLY [2 votes]: Technically this statement is wrong. He could say, "The square root of a positive number is positive (by definition)". E.g. for 0 you get $\sqrt{0}=0$ which is neither positive nor negative. And for negative numbers you even get complex solutions which are neither positive nor negative nor 0.
The definite article and the singular in "the square root" is also important to imply the conventional definition of $\sqrt{}$. But more correctly he should say "the principal square root", because mathematically the expression "the square root" doesn't make sense, since there are two different roots in general.