Radical Expressions

11-10Simple Radical Equations

Overview

Isolate the radical, then square both sides. Always check for extraneous solutions.

Key ideas

  • Isolate the radical first.
  • Square both sides.
  • Substitute back to check.

Worked examples

Example 1

Problem. Solve √x = 5.

Solution. x = 25.

Example 2

Problem. Solve √(x + 3) = 4.

Solution. x + 3 = 16 → x = 13.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Solve √x = 9.

  2. 2.

    Solve √(2x) = 6.

  3. 3.

    Solve √(x − 1) = 3.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Solve: √(x + 5) = 3.

  2. 2.

    Solve: 2√(3x) = 6.