Square Root Calculator

Calculate square roots, cube roots, and nth roots with step-by-step solutions. Perfect for learning radical simplification, estimation methods, and understanding root properties.

Common Root Calculations

√25

Perfect square

= 5

∛27

Perfect cube

= 3

√72

Simplify radical

= 6√2

√2

Irrational

≈ 1.414

Root Properties & Formulas

Property	Formula	Example
Product Rule	√(a×b) = √a × √b	√(4×9) = √4 × √9 = 2 × 3 = 6
Quotient Rule	√(a/b) = √a / √b	√(16/4) = √16 / √4 = 4 / 2 = 2
Power Rule	(√a)² = a	(√5)² = 5
Nth Root	ⁿ√(aᵐ) = a^(m/n)	³√(8²) = 8^(2/3) = 4

Perfect Squares

√1 = 1

√36 = 6

√4 = 2

√49 = 7

√9 = 3

√64 = 8

√16 = 4

√81 = 9

√25 = 5

√100 = 10

Perfect Cubes

∛1 = 1

∛64 = 4

∛8 = 2

∛125 = 5

∛27 = 3

∛216 = 6

Practical Applications

Geometry

Calculate side lengths of squares, diagonals of rectangles, and distances between points using the Pythagorean theorem.

Statistics

Calculate standard deviation, root mean square values, and other statistical measures that involve square roots.

Physics

Calculate velocities, accelerations, and other physical quantities that involve root calculations in formulas.

Construction

Calculate diagonal measurements, roof slopes, and material quantities for construction and home improvement projects.

Finance

Calculate compound interest rates, volatility measures, and risk assessments in financial mathematics.

Education

Learn and practice radical simplification, understand irrational numbers, and solve algebraic equations.