## Equations with Square Roots

Summary

To solve equations involving square roots on the GRE, it's essential to square both sides of the equation, isolate the radical if necessary, and be vigilant about the possibility of extraneous roots.

- Squaring both sides of an equation is a fundamental step in solving equations that include square roots.
- Isolating the radical on one side of the equation is crucial before squaring, especially if the radical is not alone.
- Extraneous roots can emerge from the process of squaring, necessitating a check of each solution against the original equation to verify its validity.
- The process of solving these equations can lead to no solution, especially if the solution results in the square root of a negative number.
- Practical examples illustrate the necessity of checking potential solutions to ensure they do not result in mathematical errors or fall outside the real number system.

Chapters

00:01

Understanding Square Root Equations

00:32

The Process of Squaring Both Sides

02:17

The Concept of Extraneous Roots

02:58

Solving and Verifying Solutions

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