Solve equations with square and cube roots by isolating the radical, raising both sides to the appropriate power, and checking for extraneous solutions.
Step 1 — Isolate the radical on one side of the equation so only the radical expression remains.
Step 2 — Raise both sides to the power equal to the index: square both sides for √, cube both sides for ∛.
Step 3 — Solve the resulting linear or quadratic equation using standard algebra techniques.
Step 4 — CHECK every solution in the original equation. Squaring can introduce extraneous solutions that do not satisfy the original.
√(x²) = |x|, not x
When you square both sides of an equation, you use the identity (√u)² = u. But squaring also makes negative values positive, so the equation may gain solutions that work after squaring but fail in the original.
For example, squaring √x = −3 gives x = 9, but √9 = 3 ≠ −3. So x = 9 is extraneous.
One-on-one Algebra 2 tutoring builds real fluency with radical equations, extraneous solutions, and all the techniques that show up on quizzes and finals.