$Radical Equations$

Radical Equations

Solve equations with roots: the conditions, raising to a power and a check of each root, step by step.

What to find:

√P(x) = Q(x)

√P(x) = √R(x)

√P(x) ± √R(x) = c

∛P(x) = Q(x)

Polynomials in x up to degree 4: x^2 − 3x + 1, 2x + 5, x/2. Do not type the root sign, enter only the expression under it.

The radical equation calculator solves equations with square and cube roots: it finds the conditions, removes the roots and checks every root it finds.

The main rule

Squaring can create extra roots, because a² = b² also holds when a = −b. So every root must be checked in the original equation.

Example. √(x + 5) = x − 1. Condition: x − 1 ≥ 0. Squaring gives x² − 3x − 4 = 0 with roots 4 and −1. The value −1 does not fit because the right side is negative. Answer: x = 4.