MathAlgebraHigh frequency
SAT Math: Solving Radicals with Extraneous Solutions
37+ practice questions in Praczo
What you need to know
The concept, explained
- 1
When solving an equation with a square root, you must square both sides to eliminate the radical.
- 2
Squaring both sides can introduce "extraneous solutions" — math answers that don't actually work in the original equation.
- 3
Any time you square both sides of an equation with a variable on both sides, you MUST plug your final answers back into the ORIGINAL equation to verify them.
- 4
Remember, the principal square root symbol (√) on the SAT always implies the POSITIVE root.
Common mistakes
- ✗ Failing to plug answers back in and selecting a choice that includes an extraneous solution.
- ✗ Squaring a binomial incorrectly (e.g., expanding (x - 3)² as x² + 9 instead of x² - 6x + 9).
Try a sample question
SAT-style practice
Solve for x: √(x + 2) = x
37+ questions ready to practice
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