What is a simplified radical form?

Simplified radical form writes √n as a·√b where b contains no perfect-square factor greater than 1. For example, √72 = 6√2 because 72 = 36×2 and √36 = 6.

Can I calculate the square root of a decimal?

Yes. Enter any non-negative decimal (e.g. 2.5) and the calculator returns its decimal square root. Radical simplification only applies to positive integers.

What happens if I enter a negative number?

Square roots of negative numbers are not real numbers. The calculator will show an inline error prompting you to enter a non-negative value.

How precise is the decimal result?

Results are computed using JavaScript's 64-bit IEEE 754 double precision, giving about 15–17 significant digits. The display rounds to 10 significant figures for readability.

What is a perfect square?

A perfect square is an integer whose square root is also an integer — for example 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Square Root Calculator

Enter any non-negative number to get its square root as a decimal and in simplified radical form.

Enter a Number

Number

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Result

Enter a number to see its square root

Summary

This square root calculator computes the square root of any non-negative real number instantly in your browser. It shows the result as a high-precision decimal and, for integers, also reduces the radical to its simplest form (e.g. √48 = 4√3). No server calls, no sign-up — pure client-side math.

How it works

Type a non-negative number into the input field.
The calculator checks whether the number is a perfect square and displays the exact integer root if so.
For non-perfect-square integers the radical is simplified by factoring out the largest perfect-square factor.
The high-precision decimal result is shown rounded to 10 significant figures.
Click "Copy Result" to copy the decimal value to your clipboard.

Use cases

Quickly find the square root of any number without a physical calculator.
Simplify radical expressions for algebra homework or exam prep.
Verify whether a number is a perfect square.
Convert a surd to decimal form for numerical computation.
Check simplified radical answers produced by a CAS or textbook.
Compute approximate distances using the Pythagorean theorem.

Frequently Asked Questions

Last updated: 2026-05-28 · Reviewed by Nham Vu