Question 382492
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.<br>
The notation we use for square roots are:
{{{sqrt(x)}}} is the positive square root and
{{{-sqrt(x)}}} is the negative square root.
{{{0+-sqrt(x)}}} is a reference to both square roots! (Note: The zero in front does <b>not</b> belong there! But Algebra.com's software will not let me use the "plus or minus" symbol without something in front of it.)<br>
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.