SOLUTION: Why can't square roots be negative?

Question 382492: Why can't square roots be negative?
Found 2 solutions by jsmallt9, richard1234:
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!
For any positive number there are two numbers you can square to get that number. For example there are two numbers you can square to get 9: 3 and -3. In general, for some positive number we will call "x", the two numbers you can square to get x are called the square roots of x. One is the positive square root and the other is called the negative square root. The positive square root of 9 is 3 and the negative square root of 9 is -3.

The notation we use for square roots are:
is the positive square root and
is the negative square root.
is a reference to both square roots! (Note: The zero in front does not belong there! But Algebra.com's software will not let me use the "plus or minus" symbol without something in front of it.)

I myself have used the phrase "square roots must be positive". But what I (and others) mean by this is: "When you read or write a square root (without a minus in front) you are reading and writing about a positive number. Without the minus sign in front you are reading or writing a reference to the positive square root.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Normally, square roots denote the positive root only, and to put the negative root we just use .
However, square roots of negative numbers (e.g. ) are usually expressed as (omit the zero, I get weird output without it), probably because we can't easily classify complex numbers as positive or negative.
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