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Equations with Square Roots

Mike McGarry
Lesson by Mike McGarry
Magoosh Expert
Summary
The essence of solving equations with square roots on the GMAT involves understanding the process of squaring both sides to undo the radical, being mindful of extraneous roots, and the necessity of isolating the radical before squaring.
  • Squaring both sides is the primary method to undo the radical in an equation, 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.
  • Isolating the radical on one side of the equation is a necessary step before squaring, especially when the radical is not alone.
  • Extraneous roots can arise even when the algebra is performed correctly, highlighting the importance of solution verification.
  • In cases where squaring leads to a quadratic equation, it's common to find two roots, requiring careful checking to identify any that are extraneous.
Chapters
00:00
Understanding Square Root Equations
02:17
The Challenge of Extraneous Roots
02:58
Solving and Verifying Solutions
06:52
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

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