Practice Radical Equations in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Equations with a variable under a radical sign, solved by isolating the radical, squaring both sides, 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
easySolve \sqrt{x + 3} = 5.
Example 2
hardSolve \sqrt{2x + 1} = x - 1.
Example 3
easySolve \sqrt{x} = 7.
Example 4
mediumSolve \sqrt{3x - 2} = 4.