Study Guide: Section 13-4

Solving Radical Equations

Solve radical equations (equations containing radicals with variables in the radicand) as follows:

  1. Isolate the radical on one side of the equation.
  2. Square each side of the equation to eliminate the radical.
  3. Solve the resulting equation.
  4. Always check each solution by substituting it into the original equation to identify extraneous roots.

Example: Solving a Radical Equation

Example: Solving a Radical Equation

Check the solution by substituting 8 into the original equation: √(8 + 1) = 3 &implies; √9 = 3 (True).

Practice Problems

Directions: Solve each equation. Check your solution.

Problems 1-3

Answers 1–3: 8;  16;  −23

Problems 4-6

Answers 4–6: ∅ (empty set);  1/2, −4/3;  −1/6, 1/6

Problems 7-9

Answers 7–9: ∅ (empty set);  ∅ (empty set);  1

Problems 10-12

Answers 10–12: 5;  ∅ (empty set);  −7