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Equations with Square Roots

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.
Understanding Square Root Equations
The Process of Squaring Both Sides
The Concept of Extraneous Roots
Solving and Verifying Solutions

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If you would like a more detailed explanation of what square roots are, please see:

Square Roots