Square Root Calculator

Get the square root of any number as a decimal, and — for whole numbers — in simplified radical form like 6√2.

Square root
Simplified radical
Perfect square?

How to Simplify a Square Root

Enter a number to get its square root and simplified radical.

1

Enter the number

Type any non-negative number. Whole numbers also get a simplified radical; decimals get the decimal root only.

2

Read the decimal root

The principal (positive) square root is shown first, rounded for display.

3

Read the radical form

For a whole number, the root is written as a coefficient times a smaller radical, like √72 = 6√2, by pulling out perfect-square factors.

Frequently Asked Questions

How do you simplify a square root?
Factor out the largest perfect square. For √72, 72 = 36 × 2, and √36 = 6, so √72 = 6√2. This calculator finds those factors for you.
What is the square root of a negative number?
A negative number has no real square root, because squaring any real number gives a result of zero or above. Its root is imaginary instead, so √(−9) is written 3i, where i is defined by i² = −1. This calculator works with real numbers only, so it reports a negative input as having no real root. Cube roots behave differently, since the cube root of −8 is −2, a perfectly ordinary real number.
What is a perfect square?
A perfect square is a whole number whose square root is also a whole number, such as 16 (4²) or 81 (9²). The calculator tells you whether the value you entered is one. The first few are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. Any number that is not a perfect square has an irrational square root, so √2 = 1.41421… never terminates or repeats.
Is my data sent anywhere?
Nothing you type is sent anywhere. The square root calculator runs entirely in your browser with JavaScript, so the number you enter never leave your device. There is no account, no upload step and nothing is logged. The page keeps working offline once it has loaded.