Extraneous solution
SAT glossary · Math
Definition
A value produced by a legal algebraic step (squaring, clearing denominators) that fails in the original equation. Radical and rational equations require checking every candidate; keeping an extraneous root is a planted error.
Extraneous solution in plain English
An extraneous solution is a sneaky fake answer that pops out of doing completely legal algebra steps — like squaring both sides of an equation, or clearing out denominators — but that turns out NOT to actually work when you plug it back into the ORIGINAL equation. This happens most often with equations involving square roots or fractions, because those specific moves (squaring, multiplying by an expression) can accidentally introduce new 'solutions' that were never really there. That's why, whenever you solve one of these equation types, checking every candidate answer against the original equation isn't just good practice — a question can deliberately plant an extraneous root as a wrong-answer trap, banking on you skipping that final check.
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