Root calculator
Square roots, cube roots and any nth root, with simplified radicals.
About this calculator
This root calculator finds square roots, cube roots and any other root of a number.
For whole numbers it also simplifies the radical, which is how answers are usually written in maths homework.
How it works
The nth root of x is the number that gives x when raised to the power n. Whole numbers are simplified by taking out every factor that appears n times, so √72 = √(36 × 2) = 6√2.
Last reviewed:
Worked example
- Number: 72
- Root: Square
√72: 8.48528137424
Common questions
What is a square root?
A number that gives the original number when multiplied by itself. √49 = 7, because 7 × 7 = 49.
Can you take the square root of a negative number?
Not as a real number. Square roots of negatives are imaginary numbers. Odd roots, like cube roots, of negatives are fine: ∛−8 = −2.
How do I simplify a square root?
Find the largest perfect square that divides the number. √50 = √(25 × 2) = 5√2.
The story behind it
Where the idea came from: The √ symbol first appeared in print in 1525, in a German algebra book by Christoph Rudolff.
Babylonian scribes were already finding square roots to many decimal places nearly 4,000 years ago. Rudolff's tick-like symbol, thought to come from a small r for radix, root, is still the one we use.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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