**Equations with Square Roots**

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 when other terms are present.

- Squaring both sides of an equation is the primary method to undo a square root, but this can introduce extraneous roots that don't satisfy the original equation.
- It's crucial to check each solution by substituting it back into the original equation to verify its validity, as not all algebraic solutions may work.
- When a radical is accompanied by other terms on one side of the equation, it's necessary to isolate the radical before squaring both sides to effectively solve the equation.
- Extraneous roots arise even when algebra is correctly applied, highlighting the importance of solution verification.
- Practical examples demonstrate that squaring both sides can lead to equations with no real solutions, especially when the result involves the square root of a negative number.

Chapters

00:00

Introduction to Radical Equations

00:31

Squaring Both Sides and Extraneous Roots

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: