The equation √(x + 5) = 3 looks harmless — square both sides, x + 5 = 9, x = 4, done. But radical equations have a notorious trapdoor: squaring both sides can manufacture solutions that don't actually work. Solve √(x) = −2 by squaring and you get x = 4, yet √4 = 2, not −2 — the "solution" is an extruder, an extraneous root born from the squaring step itself. Squaring erases sign information (both 2² and (−2)² equal 4), so every answer from a radical equation must be plugged back into the original to prove it belongs.

The standard attack plan: isolate the radical on one side first, then square. For √(2x + 1) + 1 = 6, subtract 1 to get √(2x + 1) = 5, square to get 2x + 1 = 25, solve x = 12, and verify: √25 + 1 = 6 ✓. Equations with two radicals need two rounds of isolate-and-square. This calculator checks your radical equation work: enter the two key values from your solving steps and confirm the computed result. The non-negotiable final step is the plug-back — it's the only thing standing between you and an extraneous root on a graded test.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Radical Equation Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.