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.
Solve √x = 9.
- 2.
Solve √(2x) = 6.
- 3.
Solve √(x − 1) = 3.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve: √(x + 5) = 3.
- 2.
Solve: 2√(3x) = 6.