FreeToolStation

Square Root Calculator

Square roots to full precision, simplified where possible.

Math Calculators Free, no sign-up Runs in your browser
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Square root
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Simplified form
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The number squared
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Perfect square
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Cube root

About the Square Root Calculator

Square Root Calculator gives the square root of a number to as many decimal places as you ask for, and shows the simplified radical form where one exists. The simplification is the part a phone calculator will not do: the square root of 72 is 8.485281..., but it is also exactly six root two, and in algebra the second form is the answer.

The simplification works by pulling out the largest perfect square that divides the number. For 72 that is 36, leaving root two outside, hence six root two. Numbers with no square factor, such as 15 or 23, cannot be simplified and are reported as they are rather than being dressed up.

Negative numbers are refused rather than returning an error code. There is no real square root of a negative number, and the calculator says so while giving the imaginary magnitude, which is usually what you were after if you got there deliberately.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

Looking for something this does not cover? FreeToolStation.com is a second collection of the same kind of everyday tools, and it is worth a look if square root calculator is only part of what you are working on.

How to use the Square Root Calculator

  1. Enter number and decimal placesDecimals are fine, and thousands separators are accepted and ignored.
  2. Read the square root, simplified form and the number squaredThe figures update as you type. The Calculate button is there if you would rather press something, but nothing waits for it.
  3. Copy or check the resultCopy the summary with the copy button, or read the formula with your own numbers in it.

Features

  • Shows square root, simplified form, the number squared, perfect square and cube root together, so you are not running it twice
  • Prints the formula with your own figures substituted in
  • Updates as you type, with no button to press and no page reload
  • Copy the result in one click
  • Free, no sign-up, and it runs entirely in your browser

Who uses this tool

The square root calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

  • Simplifying a surd for an algebra answer
  • Getting a root to a specific number of decimal places
  • Checking whether a number is a perfect square
  • Finding the side of a square from its area

Frequently asked questions

What does simplified radical form mean?

Writing a root with the largest possible perfect square taken outside it. The square root of 72 becomes 6 root 2, which is exact, where a decimal is only an approximation.

Why can I not take the root of a negative number?

Because no real number multiplied by itself gives a negative result. The answer exists in the complex numbers as an imaginary value, and the calculator reports its magnitude.

How precise is the result?

Up to fourteen decimal places, which is the limit of double-precision floating point. Beyond that the digits would not be meaningful.

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Checked and rebuilt on 2026-10-14. The method this calculator uses is described in the section above, and corrections go through the contact page.