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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The Principal Root is the positive root obtained by taking an even $n_{th}$ root of a positive number. Below are two examples. $9 =+3416 =+2$ However, when an even $n_{th}$ 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. $x_{2}=9$ To solve for $x,$ the square root must be applied to both sides of the equation. $x_{2} =9 $ The values of $x$ that make the above equation true are $3$ and $-3.$ $x=±3$ When deciding whether to use the Principal Root, consider the following rule. If the given problem has an even $n_{th}$ root written, the Principal Root should be used. In contrast, if during the problem an even $n_{th}$ 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 $nx $ to behave as a function. For example, by defining that $x $ 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.