Solving radical equations

Math

Definition

Finding the value of the variable in equations that contain square roots or other radicals. The key technique is isolating the radical and then raising both sides to the appropriate power. Extraneous solutions are common and must be checked.

How It Works

  1. Isolate the radical expression on one side of the equation.
  2. Raise both sides to the power that eliminates the radical (e.g., square both sides for a square root).
  3. Solve the resulting equation.
  4. Check all solutions in the original equation to eliminate extraneous solutions.

Examples

  • √(x + 3) = 5 → x + 3 = 25 → x = 22
  • √(2x − 1) = x − 2 → 2x − 1 = x² − 4x + 4 → x² − 6x + 5 = 0 → x = 5 or x = 1 (check: only x = 5 works)

Related Terms

Simplifying radicals Operations with radicals Nth roots Rational exponents

Study This Concept

Practice solving radical equations with free review games in these units:

Algebra 1 Unit 9: Radical Expressions Algebra 2 Unit 6: Radical Functions