Square Root Equation Solver
Solve √(ax + b) = c with visible algebra and an original-equation check. The verification step catches impossible and extraneous results.
Written and checked by TheToolNet Editorial Team · Last reviewed: September 19, 2026
Solve √(ax + b) = c
How to solve square root equations
- Isolate the radical on one side.
- Square both sides once.
- Solve the resulting equation.
- Substitute each candidate into the original equation.
For √(2x + 1) = 5, squaring gives 2x + 1 = 25, so x = 12. The check √(2·12 + 1) = √25 = 5 confirms the solution.
Why extraneous solutions happen
Squaring loses sign information: 3² and (−3)² are both 9. As a result, an equation produced after squaring can accept a value the original equation rejects. Also, the principal square root is never negative; √(expression) = −2 has no real solution even though squaring both sides would produce a candidate.
Frequently asked questions
Does this solver handle multiple radicals?
No. It is deliberately focused on one square root containing a linear expression. Multiple radicals may require repeated isolation and squaring.
What if the coefficient a is negative?
It is supported. The final candidate still must make the radicand nonnegative and satisfy the original equation.
Can I solve roots without a calculator?
For numerical roots, see how to calculate square roots quickly.