# What are extraneous roots?

#### Understand the Problem

The question is asking for a definition and explanation of what extraneous roots are, particularly in the context of mathematics and solving equations. Extraneous roots are solutions that appear in the process of solving an equation but do not satisfy the original equation.

#### Answer

A solution to a transformed equation that is not valid for the original equation.

An extraneous root is a solution to a transformed equation that is not a valid solution to the original equation.

##### Answer for screen readers

An extraneous root is a solution to a transformed equation that is not a valid solution to the original equation.

#### More Information

Extraneous roots occur when algebraic manipulations during the solution process, such as squaring both sides of an equation, introduce solutions that do not satisfy the original equation.

#### Tips

A common mistake is not checking if the solution of a transformed equation is valid for the original equation.

#### Sources

- Extraneous Root Definition (Illustrated Mathematics Dictionary) - mathsisfun.com
- Extraneous Root: Definitions and Examples - Club Z! Tutoring - clubztutoring.com
- Extraneous Solutions - Varsity Tutors - varsitytutors.com