Skip to content
Kordu Tools
Math & Numbers Runs in browser Updated 30 Mar 2026

Square Root Calculator

Calculate square roots, cube roots, and any nth root with simplified radical form and decimal precision up to 15 places.

√(?) = —

6
215

Root Formulas

√x = x^(1/2)  —  square root

∛x = x^(1/3)  —  cube root

√[n](x) = x^(1/n)  —  nth root

Simplification: Factor out the largest perfect nth power. For example, √72 = √(36 × 2) = 6√2.
Loading rating…

How to use Square Root Calculator

  1. Enter a number

    Type the number you want to find the root of. Decimals and negatives are supported.

  2. Choose the root degree

    Select square root (n=2), cube root (n=3), or type any custom root degree.

  3. Read the decimal result

    The root appears as a decimal with precision you can adjust from 2 to 15 decimal places.

  4. Read the simplified radical form

    See the result expressed in simplified radical form — for example, √72 = 6√2.

  5. Check for perfect squares

    When the result is a whole number, the calculator labels it as a perfect square or cube.

Square Root Calculator FAQ

What is the square root formula?
The square root of n is the number x such that x² = n. Written √n or n^(1/2). Example: √25 = 5 because 5² = 25.

How do I calculate a square root?
Enter the number and select square root mode. For manual calculation: use the long division method or estimate using nearby perfect squares.

How do I simplify a square root?
Factor out the largest perfect square from under the radical. Example: √72 = √(36×2) = √36 × √2 = 6√2.

What is a perfect square?
A number whose square root is a whole integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

How do I calculate a cube root?
Set the root degree to 3. Cube root of n is the number x such that x³ = n. Example: ∛27 = 3.

What is an nth root?
The nth root of x is the number y such that y^n = x. Written ⁿ√x or x^(1/n). Set a custom degree for any root.

What is the square root of a negative number?
For even roots (√, ⁴√, etc.) of negative numbers, the result is imaginary. √−4 = 2i. The tool shows a complex number hint. Odd roots of negatives are real: ∛−8 = −2.

What is the square root of 2?
√2 ≈ 1.41421356... It is an irrational number with infinitely many non-repeating decimal places.

How precise are the results?
The tool provides up to 15 decimal places of precision, adjustable via the precision control.

Is any data sent to a server?
No. All calculations run entirely in your browser. Nothing is uploaded or stored.

Background

Find the square root, cube root, or any nth root of a number with full precision. Results show both the simplified radical form and the decimal approximation to a configurable number of decimal places (2 to 15). Simplified radical form extracts perfect square factors — for example, √72 = 6√2 — which is required in many algebra and geometry problems. Detects perfect squares and cubes and labels them clearly. Handles negative inputs correctly: odd roots of negatives return real results (∛−8 = −2), even roots of negatives display a complex number hint (√−4 = 2i). Custom root degree lets you calculate any nth root beyond square and cube. Useful for geometry, algebra, physics, and engineering. All processing runs in your browser.

Related tools

Scientific Calculator

A full-featured scientific calculator with trigonometry, logarithms, exponents, roots, memory functions, and calculation history. Full keyboard support.

Exponent & Power Calculator

Calculate any base raised to any power, including negative and fractional exponents, with scientific notation and power rules reference.

Quadratic Equation Solver

Solve ax² + bx + c = 0 with real or complex roots, discriminant, vertex form, axis of symmetry, and a step-by-step parabola graph.

Logarithm Calculator

Calculate log base 10, natural log (ln), log base 2, or any custom base. Antilog mode and logarithm rules reference included.

Percentage Calculator

Calculate X% of Y, find what percentage X is of Y, or compute percentage increase and decrease. Results update as you type.