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Equations with Square Roots

The essence of solving equations with square roots on the GRE involves understanding the process of squaring both sides to undo the radical, while being cautious of extraneous roots that may arise from the algebraic process.
  • Squaring both sides is the primary method to undo square roots in equations, but this can introduce extraneous roots that don't satisfy the original equation.
  • It's crucial to check each solution by substituting back into the original equation to verify its validity, as not all algebraic solutions may work.
  • When dealing with radicals, isolating the radical on one side of the equation is necessary before squaring both sides to ensure a correct simplification process.
  • Extraneous roots can arise even if the algebra is performed correctly, highlighting the importance of solution verification.
  • Practical examples demonstrate that equations involving square roots can have one, both, or no solutions, emphasizing the need for careful analysis and verification of each potential solution.
Introduction to Equations with Square Roots
Understanding Extraneous Roots
Solving and Verifying Solutions
Isolating the Radical Before Squaring

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

Square Roots