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Square Root Calculator

Square roots, cube roots and any nth root, exact or decimal.

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Which root?

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Perfect squares and their roots

nn²√n∛n

Quick Tool Overview

The Square Root Calculator gives the square root of any number as a decimal and, where one exists, in exact simplified surd form. The square root of 72 is not just 8.485 — it is 6 times the square root of 2, which is the form an exam answer usually wants. Cube roots and any nth root are handled in the same panel.

What it does
Finds square, cube and nth roots in decimal and exact form
You give it
A number and the root you want
You get back
The decimal value plus the simplified surd where one exists
Best for
Algebra homework, exam answers and geometry work
Calculators Free, unlimited use No sign-up Runs in your browser

About the Square Root Calculator

Enter a number to get its square root as a decimal and, where one exists, in exact simplified surd form. The square root of 72 is not just 8.485; it is 6 times the square root of 2, and that is the form an exam answer usually wants.

The same panel handles cube roots and any nth root, so you can find the fourth root of 625 or the fifth root of 1,024 without reaching for fractional exponents. Perfect squares and perfect cubes are flagged when you hit one, negative numbers are explained rather than silently failing, and a reference list of the common squares and roots sits below the calculator for the values worth memorising.

Key features of the Square Root Calculator

Exact surd form

Roots are simplified to the form an exam expects, not just rounded to three decimal places.

Any nth root

The fourth root of 625 or the fifth root of 1,024 without reaching for fractional exponents.

Perfect squares and cubes flagged

When you land on one it is called out, which is useful when you are checking whether a number factors cleanly.

Negative numbers explained

Rather than failing silently, the calculator explains why a real square root does not exist.

Reference table

The common squares and roots worth memorising are listed below the calculator.

How to use the Square Root Calculator

  1. 1

    Enter your number

    Type any positive number, whole or decimal. The root is calculated as you type.

  2. 2

    Choose the root

    Square root is the default. Switch to cube root, or set any nth root you need.

  3. 3

    Read the exact form

    Where a square root simplifies to a whole number times a surd, that exact form is shown alongside the decimal.

Frequently asked questions

Pull out the largest perfect square factor. For the root of 72, the largest perfect square factor is 36, so it becomes the root of 36 times the root of 2, which is 6 root 2.

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