Practice Radical Equations in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Solving equations that contain variable expressions under a radical by isolating the radical, raising both sides to the appropriate power to eliminate it, solving the resulting equation, and checking for extraneous solutions.

A radical 'traps' the variable inside a square root. To free it, isolate the radical on one side, then square both sides to undo the square root. But squaring can introduce fake solutions (extraneous solutions) that do not actually satisfy the original equation, so you MUST check every answer.

Example 1

easy
Solve \sqrt{x + 3} = 5.

Example 2

hard
Solve \sqrt{2x + 1} = x - 1.

Example 3

easy
Solve \sqrt{x} = 7.

Example 4

medium
Solve \sqrt{3x - 2} = 4.