Radical Calculator

Simplify radicals, square roots, cube roots, and nth roots with step-by-step solutions. Prime factorization, perfect power extraction, and decimal approximations.

Example Radicals

Square Roots

Cube Roots

Higher Roots

Perfect Powers

Radical Input

Operation Type

Radicand (number under radical)

Index (root type)

Expression:

√18

Common Indices:

• Index 2: Square root (√)

• Index 3: Cube root (∛)

• Index 4: Fourth root (⁴√)

• Index n: nth root (ⁿ√)

Radical Properties

Product Rule:

ⁿ√(ab) = ⁿ√a × ⁿ√b

Quotient Rule:

ⁿ√(a/b) = ⁿ√a / ⁿ√b

Power Rule:

ⁿ√(aᵐ) = a^(m/n)

Root of Root:

ᵐ√(ⁿ√a) = ᵐⁿ√a

Applications

Geometry:

Distance calculations, Pythagorean theorem, area formulas.

Physics:

Wave equations, quantum mechanics, relativity calculations.

Engineering:

Signal processing, structural analysis, optimization.

Finance:

Compound interest, risk calculations, portfolio theory.