When do I need to check for extraneous roots?

On the GMAT, you need to worry about extraneous roots only when doing one of two things:

1. Squaring a variable
2. Getting rid of the absolute value of a variable.

How to work through these calculations is covered in the relevant lesson videos :)

If the equation you're given already includes the squared variable (and you don't multiply by the variable yourself), then you don't need to worry about the extraneous root. Both solutions will be correct because the variable was already squared.

You only need to worry about the extraneous root in the case of a quadratic equation if you made the equation quadratic by multiplying by a variable. Any time you square a negative number or a variable (which may be negative), you risk losing information by making it positive. That means that, if you square a variable (watch out especially for variables on both sides of the equation, which can easily hide a negative) or a negative number, you should always do a quick plug-in and check.

Here's a post that further covers the topic of extraneous roots:

• GMAT Math: Algebra Equations with Radicals