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SAT Math: Solving Radical Equations
24+ practice questions in Praczo
What you need to know
The concept, explained
- 1
To solve √(expression) = value, isolate the radical, then square both sides to eliminate it.
- 2
Always check for extraneous solutions — squaring both sides can introduce solutions that do not satisfy the original equation.
- 3
If the radical is not isolated before squaring, you'll create extra terms that complicate the equation.
- 4
Substitute each solution back into the original equation to verify it works.
- 5
Fractional exponents and radicals are equivalent: x^(1/2) = √x, x^(1/3) = ∛x.
Common mistakes
- ✗ Skipping the check for extraneous solutions — a valid algebraic solution may be invalid in the original equation.
- ✗ Squaring both sides incorrectly: (√x + 3)² ≠ x + 9. You must expand the entire left side.
Try a sample question
SAT-style practice
What is the solution to √(2x + 3) = x?
24+ questions ready to practice
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