Square-root equation solver
Solve supported square-root equations, including a linear term outside the radical and equations with one square root on each side, then reject extraneous roots.
Try an example
This solver focuses on square-root equations that reduce to a linear or quadratic equation after a safe squaring step. It supports forms such as √(x + 1) + 3 = 7, x + √(x + 1) = 5, and √(2x + 3) = √(x + 8).
Nested radicals, cube roots, and equations that need repeated radical isolation remain outside the current scope. I prefer an explicit unsupported result to silently applying an invalid transformation.
When there is one square-root term, I isolate it before squaring. When each side is a single square root, squaring compares the two radicands directly. The derived equation is then solved with the existing linear or quadratic solver.
Squaring can introduce roots that were never valid in the starting equation, so every candidate is substituted back into the original radical equation before it is accepted.
Type or paste an equation, solve it, inspect the transformations, and use verification and the graph instead of relying on the final value alone.
√(2x + 3) = 5√(x + 1) + 3 = 7x + √(x + 1) = 5√(2x + 3) = √(x + 8)Follow the same steps the calculator uses for three equations in this category.
x = 11
Square both sides to remove the square root
sqrt(2*x+3)=5 → 2x+3=(5)^2
Add 22 to both sides
2x-22=0 → 2x=22
Divide both sides by 2
2x=22 → x=11
Check candidate roots in the original radical equation
x=11 → x=11
Verified
x = 15
Square both sides to remove the square root
sqrt(x+1)+3=7 → x+1=(4)^2
Add 15 to both sides
x-15=0 → 1x=15
Check candidate roots in the original radical equation
x=15 → x=15
Verified
x = 3
Square both sides to remove the square root
x+sqrt(x+1)=5 → x+1=(-x+5)^2
Factor the quadratic expression
-x^2+11x-24=0 → -(x-3)(x-8)=0
Use the zero-product property to solve each factor
-(x-3)(x-8)=0 → x=3 or x=8
Check candidate roots in the original radical equation
x=3 or x=8 → x=3
Verified
Substitute each answer into the original equation and compare both sides.
Cubic and higher-degree polynomials, logarithmic, exponential, trigonometric, nested-radical, and multiple-absolute-value equations remain outside the supported solver scope.