The Principal Root is the positive root obtained by taking an even root of a positive number. Below are two examples. However, when an even root is applied to an equation to undo a power, the root takes both positive and negative values. As an example, consider the following equation. To solve for the square root must be applied to both sides of the equation. The values of that make the above equation true are and When deciding whether to use the Principal Root, consider the following rule. If the given problem has an even root written, the Principal Root should be used. In contrast, if during the problem an even root must be applied to both sides of the equation, then this root can be positive or negative.
The Principal Root exists because it allows to behave as a function. For example, by defining that equals a positive number only, it has only one output for each input.
The Principal Root is the positive root because the positive root is more practical than the negative root.